Solve without a calculator: If $x+sqrt{x}=13$ then $x+frac{13}{sqrt{x}}=?$

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$$x+sqrt{x}=13$$
$$x+frac{13}{sqrt{x}}=?$$

I tried to square(and also triple in another attempt) both sides of both of the equations hoping that I would find some expression to plug in. It didn't help.

Then, I tried to simply bring the second equation to a common denominator.It didn't help neither.

Then I found the $x$ value ($9.86$) from the first equation by using a calculator and then plugged in to the second equation and got this expression
$$frac{493}{50}+65sqrt{frac{2}{493}}$$

Now, Is this question solvable without a calculator?

edited Nov 23 at 17:52

Math Lover

13.7k31435

asked Nov 23 at 16:48

Eldar Rahimli

385

add a comment |

up vote
0
down vote

favorite

$$x+sqrt{x}=13$$
$$x+frac{13}{sqrt{x}}=?$$

I tried to square(and also triple in another attempt) both sides of both of the equations hoping that I would find some expression to plug in. It didn't help.

Then, I tried to simply bring the second equation to a common denominator.It didn't help neither.

Then I found the $x$ value ($9.86$) from the first equation by using a calculator and then plugged in to the second equation and got this expression
$$frac{493}{50}+65sqrt{frac{2}{493}}$$

Now, Is this question solvable without a calculator?

edited Nov 23 at 17:52

Math Lover

13.7k31435

asked Nov 23 at 16:48

Eldar Rahimli

385

add a comment |

up vote
0
down vote

favorite

$$x+sqrt{x}=13$$
$$x+frac{13}{sqrt{x}}=?$$

I tried to square(and also triple in another attempt) both sides of both of the equations hoping that I would find some expression to plug in. It didn't help.

Then, I tried to simply bring the second equation to a common denominator.It didn't help neither.

Then I found the $x$ value ($9.86$) from the first equation by using a calculator and then plugged in to the second equation and got this expression
$$frac{493}{50}+65sqrt{frac{2}{493}}$$

Now, Is this question solvable without a calculator?

edited Nov 23 at 17:52

Math Lover

13.7k31435

asked Nov 23 at 16:48

Eldar Rahimli

385

$$x+sqrt{x}=13$$
$$x+frac{13}{sqrt{x}}=?$$

I tried to square(and also triple in another attempt) both sides of both of the equations hoping that I would find some expression to plug in. It didn't help.

Then, I tried to simply bring the second equation to a common denominator.It didn't help neither.

Then I found the $x$ value ($9.86$) from the first equation by using a calculator and then plugged in to the second equation and got this expression
$$frac{493}{50}+65sqrt{frac{2}{493}}$$

Now, Is this question solvable without a calculator?

algebra-precalculus radicals

edited Nov 23 at 17:52

Math Lover

13.7k31435

asked Nov 23 at 16:48

Eldar Rahimli

385

edited Nov 23 at 17:52

Math Lover

13.7k31435

asked Nov 23 at 16:48

Eldar Rahimli

385

edited Nov 23 at 17:52

Math Lover

13.7k31435

edited Nov 23 at 17:52

Math Lover

13.7k31435

edited Nov 23 at 17:52

Math Lover

13.7k31435

asked Nov 23 at 16:48

Eldar Rahimli

385

asked Nov 23 at 16:48

Eldar Rahimli

385

asked Nov 23 at 16:48

Eldar Rahimli

385

add a comment |

1 Answer
1

active

oldest

votes

up vote
12
down vote

accepted

Note that
$$x+frac{13}{sqrt{x}} = x + frac{x+sqrt{x}}{sqrt{x}} = x+sqrt{x}+1=14.$$

answered Nov 23 at 16:49

Math Lover

13.7k31435

add a comment |

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

up vote
12
down vote

accepted

Note that
$$x+frac{13}{sqrt{x}} = x + frac{x+sqrt{x}}{sqrt{x}} = x+sqrt{x}+1=14.$$

answered Nov 23 at 16:49

Math Lover

13.7k31435

add a comment |

up vote
12
down vote

accepted

Note that
$$x+frac{13}{sqrt{x}} = x + frac{x+sqrt{x}}{sqrt{x}} = x+sqrt{x}+1=14.$$

answered Nov 23 at 16:49

Math Lover

13.7k31435

add a comment |

up vote
12
down vote

accepted

Note that
$$x+frac{13}{sqrt{x}} = x + frac{x+sqrt{x}}{sqrt{x}} = x+sqrt{x}+1=14.$$

answered Nov 23 at 16:49

Math Lover

13.7k31435

Note that
$$x+frac{13}{sqrt{x}} = x + frac{x+sqrt{x}}{sqrt{x}} = x+sqrt{x}+1=14.$$

answered Nov 23 at 16:49

Math Lover

13.7k31435

answered Nov 23 at 16:49

Math Lover

13.7k31435

answered Nov 23 at 16:49

Math Lover

13.7k31435

answered Nov 23 at 16:49

Math Lover

13.7k31435

add a comment |

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