Question

The difference between two positive number is 5 and the sum of their squares is 73 find the product of this number

Answer 1

Here is the answer....

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Answer 2

$\bold\red{\underline{\underline{Answer:}}}$

$\bold{The \ product \ of \ the \ numbers}$

$\bold{is \ 24.}$

$\bold\orange{Given:}$

Difference between two positive numbers is 5.

The sum of their squares is 73.

$\bold\pink{To \ find:}$

Product of the numbers.

$\bold\green{\underline{\underline{Solution}}}$

Let two positive numbers be x and y.

According to first condition

x-y=5...(1)

According to second condition

$\bold{x^{2}+y^{2}=73...(2)}$

___________________________

From (1) and (2)

According to identity

$\bold{x^{2}+y^{2}=(x-y)^{2}+2(xy)}$

$\bold{73=5^{2}+2(xy)}$

$\bold{73=25+2(xy)}$

$\bold{73=25+2(xy)}$

$\bold{73-25=2(xy)}$

$\bold{2(xy)=48}$

$\bold{xy=\frac{48}{2}}$

$\bold{xy=24}$

Therefore,

$\bold\purple{The \ product \ of \ the \ numbers}$

$\bold\purple{is \ 24.}$