Question

The sum of two numbers is
2 and their difference is 20.
Find the product of this two
numbers​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$\sf{The \ product \ of \ the \ two \ numbers}$

$\sf{is \ -99.}$

Given:

$\sf{\leadsto{The \ sum \ of \ two \ numbers \ is \ 2}}$

$\sf{and \ their \ difference \ is \ 20.}$

To find:

$\sf{The \ product \ of \ numbers.}$

Solution:

$\sf{Let \ the \ two \ numbers \ be \ x \ and \ y.}$

$\sf{By \ identity}$

$\sf{(a+b)^{2}-(a-b)^{2}=4ab}$

$\sf{Here, \ a \ and \ b \ are \ x \ and \ y}$

$\sf{\therefore{(x+y)^{2}-(x-y)^{2}=4xy}}$

$\sf{\therefore{2^{2}-20^{2}=4xy}}$

$\sf{\therefore{4-400=4xy}}$

$\sf{\therefore{-396=4xy}}$

$\sf{\therefore{xy=\dfrac{-396}{4}}}$

$\sf{\therefore{xy=-99}}$

$\sf{The \ product \ of \ the \ two \ numbers}$

$\sf{is \ -99.}$

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Extra information:

$\sf{(a+b)^{2}+(a-b)^{2}=2(a^{2}+b^{2})}$

$\sf{(a+b)^{2}=(a-b)^{2}+4ab}$

$\sf{(a-b)^{2}=(a+b)^{2}-4ab}$