If (a^2 + b^2)\(x^2 + y^2) = (ax + by)^2; prove that a\x = b\y

Given, ⇒ (a 2 + b 2 )(x 2 + y 2 ) = (ax + by) 2 ⇒ a 2 x 2 + a 2 y 2 + b 2 x 2 + b 2 y 2 = a 2 x 2 + b 2 y 2 + 2abxy ⇒ a 2 y 2 + b 2 x 2 - 2abxy = 0 ⇒ (ay - bx) 2 = 0 ⇒ ay - bx = 0 ⇒ ay = bx ⇒ Hence, proved that .

Mathematics

If (a² + b²)(x² + y²) = (ax + by)²; prove that $\dfrac{a}{x} = \dfrac{b}{y}$

Ratio Proportion

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Answer

Given,

⇒ (a² + b²)(x² + y²) = (ax + by)²

⇒ a²x² + a²y² + b²x² + b²y² = a²x² + b²y² + 2abxy

⇒ a²y² + b²x² - 2abxy = 0

⇒ (ay - bx)² = 0

⇒ ay - bx = 0

⇒ ay = bx

⇒ $\dfrac{a}{x} = \dfrac{b}{y}$

Hence, proved that $\dfrac{a}{x} = \dfrac{b}{y}$ .

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Mathematics

If (a² + b²)(x² + y²) = (ax + by)²; prove that $\dfrac{a}{x} = \dfrac{b}{y}$

Ratio Proportion

Answer

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