All are squared

Algebra Level 2

If, a b = c d = e f = 3 \large \dfrac{a}{b}=\dfrac{c}{d}=\dfrac{e}{f}=3

then, 2 a 2 2 b 2 = 3 c 2 3 d 2 = 4 e 2 4 f 2 = ? \large \dfrac{2a^2}{2b^2}=\dfrac{3c^2}{3d^2}=\dfrac{4e^2}{4f^2}=?

3 9 2 4

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1 solution

Viki Zeta
Oct 4, 2016

The question is made confusing, but it's easy.

a b = c d = e f = 3 Square on both the sides, ( a b ) 2 = ( c d ) 2 = ( e f ) 2 = 9 a 2 b 2 = c 2 d 2 = e 2 f 2 = 9 Multiply and divide by 2, 3, 4 in each case, so the equation will remain the same 2 a 2 2 b 2 = 3 c 2 3 d 2 = 4 e 2 4 f 2 = 9 \dfrac{a}{b} = \dfrac{c}{d} = \dfrac{e}{f} = 3 \\ \text{Square on both the sides, } \\ (\dfrac{a}{b})^2 = (\dfrac{c}{d})^2 = (\dfrac{e}{f})^2 = 9 \\ \dfrac{a^2}{b^2} = \dfrac{c^2}{d^2} = \dfrac{e^2}{f^2} = 9 \\ \text{Multiply and divide by 2, 3, 4 in each case, so the equation will remain the same} \\ \boxed{\dfrac{2a^2}{2b^2} = \dfrac{3c^2}{3d^2} = \dfrac{4e^2}{4f^2} = 9}

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