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MATH / Two positive numbers p and q have the property that their sum is equal to their product. If their difference is 7, what is (1)/((1)/(p²)+(1)/(q²))? Your answer will be of the form …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Two positive numbers

p

and

q

have the property that their sum is equal to their product. If their difference is

7

, what is

\frac{1}{\frac{1}{p^2}+\frac{1}{q^2}}

? Your answer will be of the form

\frac{a+b\sqrt{c}}{d}

, where

a

and

b

don't both share the same common factor with

d

and

c

has no square as a factor. Find

a+b+c+d

Plain-text mathematical notation (without MathML)

Two positive numbers p and q have the property that their sum is equal to their product. If their difference is 7, what is (1)/((1)/(p²)+(1)/(q²))? Your answer will be of the form (a+b√(c))/(d), where a and b don't both share the same common factor with d and c has no square as a factor. Find a+b+c+d.

Original LaTeX notation

Two positive numbers $p$ and $q$ have the property that their sum is equal to their product. If their difference is $7$, what is $\frac{1}{\frac{1}{p^2}+\frac{1}{q^2}}$? Your answer will be of the form $\frac{a+b\sqrt{c}}{d}$, where $a$ and $b$ don't both share the same common factor with $d$ and $c$ has no square as a factor. Find $a+b+c+d$.

level

Level 5

type

Algebra

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task_id: 97ee7ef6-6a41-546a-984e-926c7e89b848
task_key: algebra--test--97ee7ef6-6a41-546a-984e-926c7e89b848
task_revision_id: 2
config / split: algebra / test

Official source

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