Question

If (x+ y)² = 32 and
xy=
12. find the
value of x²+y²​

Answer 1

Answer:

xy=12.....(1)

(x+y)2=32

x2+2xy+y2=32

x2+2*12+y2=32.......from(1)

x2+y2+24=32

x2+y2=32-24

x2+y2=8.....hence proved

Step-by-step explanation:

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Answer 2

Answer:

8

Step-by-step explanation:

${(x + y)}^{2} = 32 \: and \: xy = 12 \\ \\ we \: know \: that \\ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ similarily \: here \: expanding \: we \: get \: \\ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ 32 \: = {x}^{2} + {y}^{2} + 2(12) \\ 32 = {x}^{2} + {y}^{2} + 24 \\ {x}^{2} + {y}^{2} = 32 - 24 = 8 \\ \\ {x}^{2} + {y}^{2} = 8$

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