Math, asked by unliveddoor, 4 days ago

x²+y²=89 4xy=160 find (x-y)²+2(x+y)²​

Answers

Answered by preeti353615
1

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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