solve the equation please answer
Answers
Answer:
x = a² and y = b²
Step-by-step explanation:
(b²/a)x + (a²/b)y = ab(a+b) × (1)
(b²)x + (a²)y = 2a²b² × (1/a)
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⇒ (b²/a)x + (a²/b)y = ab(a+b)
(-) (b²/a)x + (a)y = 2ab²
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⇒ (a²/b - a)y = ab[a + b - 2b]
⇒ (a² - ab)y = ab²[a-b]
⇒ a(a-b)y = a×b²×[a-b]
⇒ y = b²
substitute the value of y in equation 2
⇒ b²x + a²(b²) = 2a²b²
⇒ b²x = a²b²
⇒ x = a²
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VERIFICATION
- For equation 1
R.H.S = ab(a+b)
L.H.S = (b²/a)x + (a²/b)y
substitute the values of x and y
⇒ L.H.S = (b²/a)(a²) + (a²/b)(b²)
= b²a + a²b
= ab(a+b) = R.H.S
∵ L.H.S = R.H.S
∴ x = a² and y = b²
- For equation 2
R.H.S = 2a²b²
L.H.S = (b²)x + (a²)y
substitute the values of x and y
⇒ L.H.S = (b²)(a²) + (a²)(b²)
= 2a²b² = R.H.S
∵ L.H.S = R.H.S
∴ x = a² and y = b²
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