Question

If x² + y² =25, xy = 8
Then find the value of
x-y (b) x+ y​

Answer 1

Answer:

$i)x-y =±3\\ii) x+y =±\sqrt{41}$

Step-by-step explanation:

$x^{2}+y^{2}=25 \:--(1)$

and

xy = 8 ---(2)

Now,

i) (x-y)² = x²+y²-2xy

= 25-2×8

= 25-16

= 9

$x-y =±\sqrt{9}\\=±\sqrt{3\times 3}\\=±3$

$ii) (x+y)^{2}\\=x^{2}+y^{2}+2xy\\=25+2\times 8\\=25+16\\=41$

$x+y =±\sqrt{41}$

Therefore,

$i)x-y =±3\\ii) x+y =±\sqrt{41}$

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