If x - y =5, x + y =1, then x^2 - y^2= ?? +explanation please and thanks

Question

asked Dec 26, 2023 153k views

1 Answer

Theadriangreen · Answer 1 · 2024-01-01T03:49:31+0000

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Step-by-step explanation:

Apply the difference of squares rule

x^2 - y^2 = (x-y)(x+y)

x^2 - y^2 = (5)(1)

x^2 - y^2 = 5

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Alternatively, you can solve the system

$\begin{cases}x-y=5\\x+y = 1\end{cases}$

for x and y to get (x,y) = (3,-2).

Then compute x^2-y^2 = 3^2-(-2)^2 = 9-4 = 5