x²+y²=89 4xy=160 find (x-y)²+2(x+y)²
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Answer:
(x-y)²+2(x+y)² = 347
Step-by-step explanation:
Given:
x²+y²=89 4xy = 160
Find (x-y)²+2(x+y)²
Step:
Identity which is use
- (a +b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab +b²
(x-y)²+2(x+y)²
= x² - 2xy + y² + 2(x² + 2xy + y²)
Multiply by 2
= x² - 2xy + y² + 2x² + 4xy + 2y²
Rearrange similar terms
= x² + 2x² - 2xy + 4xy+ y² + 2y²
= 3x² + 2xy+3y²
= 3 (x² + y²)+ 2xy
Now put x²+y²=89
and 4xy=160
so 2xy = 80
= 3 (89) + 80
= 267 + 80
=347
So, (x-y)²+2(x+y)² = 347
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