Question

Solve a (x+y)+b (x -y)=a^2-ab+b ^2 and a (x+y)-b(x-y)=a ^2+ab-b ^2

Answer 1

Solution:

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Given:

a(x+y) + b(x-y) = a² - ab + b² ..(i).,

a(x+y) - b(x-y) = a² + ab - b² ...(ii)

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To find,

The values of x and y.

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Adding both the equations,

We get,

=> a(x + y) + b(x - y) + a(x + y) - b(x - y) = a² - ab + b² + a² +ab - b²

=> 2a(x + y) = 2a²

=> x + y = a ...(iii),
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Subtracting (ii) from (i),

=> a(x + y) + b(x - y) -(a(x + y)  - b(x - y)) = a² - ab + b² - (a² + ab -b²)

=> a(x + y) +  b(x - y) - a(x - y) + b(x - y) = a² - ab + b² - a² - ab + b²

=> 2b(x - y) = -2ab + 2b²

=> 2b(x - y) = 2b² - 2ab

=> 2b(x - y) = 2b(b - a)

=> x - y = b - a ..(iv)

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Adding (iii) & (iv),

We get,

=> (x + y) + (x - y) a + b- a

=> 2x = b

=> ∴ $x = \frac{b}{2}$

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Substituting value of x in (iv),

We get,

=> x - y = b - a

=> $\frac{b}{2} - y = b - a$

=> $-y = b-a- \frac{b}{2}$

=> $-y = \frac{b}{2} - a$

=> ∴ $y = a - \frac{b}{2}$

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                                         Hope it Helps!!

Answer 2

Answer:

Step-by-step explanation:

Ans.x=b2/2a

Y=2a2+b2/2ab