Question

X + y is equal to 12 and X y is equal to 32 find the value of x square + y square and x square minus y square

Answer 1

Step-by-step explanation:

x+y = 12

xy = 32

(x+y)² = x² + y² + 2xy

12² = x² + y² + 2*32

x² + y ² = 144-64

x² + y² = 80

(x-y)² = x² + y² - 2xy

(x-y)² = 80 - 2*32

(x-y) ² = 80-64

(x-y)² = 16

x-y = 4

x²-y² = (x+y)(x-y)

x²-y² = 12*4= 48

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Answer 2

Given:-

x + y = 12

xy = 32

To Find:-

x² + y² = ?

x² - y² = ?

Solution:-

x + y = 12

squaring both side

we get,

(x + y)² = (12)²

using identity (a + b)² = a²+b²+2ab

x²+ y²+2xy $\implies$144

x²+y²+2(32) $\implies$144

x²+y² $\implies$ 144 - 64

x²+y² $\implies$ 80 ......ans...

Now, (x-y)² = x²+y²-2ab

(x-y)² = 80-2(32)

(x-y)² = 80-64

x-y = $\sqrt{16}$

x-y = 4

and,

x²-y² = (x+y)(x-y)

x²-y² = 12×4

x²-y² = 48 ......ans....

$\fbox{ x²+ y² = 80}$

$\fbox{ x²- y² = 48 }$