Question

Hello pls solve the above question ​

Answer 1

x = a and y = b

Check the attached image.

Answer 2

GIVEN :

$\frac{x}{a} - \frac{y}{b} = 0............(i) \\ ax + by = {a}^{2} + {b}^{2} ..........(ii)$

SOLUTION :

★Taking eq (i) ★

$\frac{x}{a} - \frac{y}{b} = 0 \\ \implies \frac{xb - ay}{ab} = 0 \\ \implies \: xb - ay = 0 ...........(i)$

✪ Multiply a with eq(i) and b with eq(ii) ✪

$axb - {a}^{2} y = 0.......(i) \\ axb + {b}^{2} y = {a}^{2} b + {b}^{3} ........(ii)$

★ By elimination :-

$axb - {a}^{2} y = 0 \\ axb + {b}^{2} y = {a}^{2} b + {b}^{3}$

(-). (-). (-)

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- a²y - b²y = -a²b - b³

→ -y (a² + b²) = - b(a² +b²)

→ - y = - b

→. y = b

✪ Putting y = b in eq(i)✪

xb - ay = 0

→ xb - ab = 0

→ xb = ab

→ x = ab/b

→ x = a

Therefore ,

x = a

y = b

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MORE INFORMATION:

Algebraic Identity :-

★(a+b)² = a²+2ab+b²

★(a-b)² = a²-2ab+b²

★ a²- b² = (a+b)(a-b)

★ a²+b² = (a+b)²-2ab

★(a+b)²+(a-b)² = 2(a²+b²)

★(a+b)²-(a-b)² = 4ab

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