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If (x square + y square) …

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If (x square + y square) (a square+ b square) =(ax + by)^2. Prove that x/a = y/b

    • Posted by Yashika Das 4 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Ashok Kumar 4 years, 6 months ago

    We have, (x^2+y^2)(a^2+b^2)=(ax+by)^2 Prove that, \dfrac{x}{a}=\dfrac{y}{b}. ∴ (x^2+y^2)(a^2+b^2)=(ax+by)^2 ⇒ x^2(a^2+b^2)+y^2(a^2+b^2)=(ax)^2+(by)^{2} +2(ax)(by) Using algebraic identity, (x+y)^{2}=x^{2}+y^{2}+2xy ⇒ x^2a^2+x^2b^2+y^2a^2+y^2b^2=a^2x^2+b^2y^{2} +2abxy ⇒ x^2b^2+y^2a^2=2abxy ⇒ x^2b^2+y^2a^2-2abxy=0 ⇒ (xb)^2+(ya)^2-2(xb)(ya)=0 Using algebraic identity, (x-y)^{2}=x^{2}+y^{2}-2xy ⇒ (xb-ya)^2=0 ⇒ xb - ya = 0 ⇒ xb = ya ⇒ \dfrac{x}{a}=\dfrac{y}{b}, proved. Hence, \dfrac{x}{a}=\dfrac{y}{b}, proved.

    0Thank You

    Shreya Gupta 4 years, 6 months ago

    (x²+y²) (a²+b²)= (ax+by)² (a²x²+b²x²+a²y²+b²y²)=(a²x²+b²x²+2abxy) b²x²+a²y²=2axby b²x²+a²y²-2axby=0 (bx-ay)²=0 bx-ay=0 Therefore, y/b=x/a

    2Thank You

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