Question

If x - y=6 and xy = 16, find the value of x + y.​

Answer 1

Answer: xy =(x-y)(x+y)put value 16=(6)(x+y)16-6=(x+y) (x+y)=10x+y =10. . . proved answer

Answer 2

The value of x + y = ± 10

Given :

x - y = 6 and xy = 16

To find :

The value of x + y

Identity Used :

$\displaystyle \sf{ {(x + y)}^{2} = {(x - y)}^{2} + 4xy}$

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that x - y = 6 and xy = 16

Step 2 of 2 :

Find the value of x + y

$\displaystyle \sf{ {(x + y)}^{2} = {(x - y)}^{2} + 4xy}$

$\displaystyle \sf{ \implies {(x + y)}^{2} = {(6)}^{2} + 4 \times 16 }$

$\displaystyle \sf{ \implies {(x + y)}^{2} = 36 + 64 }$

$\displaystyle \sf{ \implies {(x + y)}^{2} = 100 }$

$\displaystyle \sf{ \implies {(x + y)}^{2} = {10}^{2} }$

$\displaystyle \sf{ \implies x + y = \pm \: 10}$

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