If a : b = c : d , prove that :

(6a + 7b) (3c - 4d) = (6c + 7d) (3a- 4b).

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Solution

$G i v e n a over b equals c over d M u l t i p l y i n g space e a c h space s i d e space b y space 6 over 7 fraction numerator 6 a over denominator 7 b end fraction equals fraction numerator 6 x over denominator 7 d end fraction b y space c o m p o n e n d o fraction numerator 6 a plus 7 b over denominator 7 b end fraction equals fraction numerator 6 c plus 7 d over denominator 7 d end fraction fraction numerator 6 a plus 7 b over denominator 6 c plus 7 d end fraction equals fraction numerator 7 b over denominator 7 d end fraction equals b over d rightwards arrow 1 A l s o comma a over b equals c over d m u l t i p l y i n g space e a c h space s i d e space b y space 3 over 4 fraction numerator 3 a over denominator 4 b end fraction equals fraction numerator 3 c over denominator 4 d end fraction B y space d i v i d e n d o fraction numerator 3 a minus 4 b over denominator 4 b end fraction equals fraction numerator 3 c minus 4 d over denominator 4 d end fraction fraction numerator 3 a minus 4 b over denominator 3 c minus 4 d end fraction equals fraction numerator 4 b over denominator 4 d end fraction equals b over d rightwards arrow 2 F r o m space 1 space a n d space 2 fraction numerator 6 a plus 7 b over denominator 6 c plus 7 d end fraction equals fraction numerator 3 a minus 4 b over denominator 3 c minus 4 d end fraction left parenthesis 6 a plus 7 b right parenthesis left parenthesis 3 c minus 4 d right parenthesis equals left parenthesis 6 c plus d right parenthesis left parenthesis 3 a minus 4 b right parenthesis$

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Similar questions

a : b = c : d,

(6 a + 7 b) (3 c - 4 d) = (6 c + 7 d) (3 a - 4 b)

\frac{a}{b} = \frac{c}{d}

\frac{3 a^{2} + 4 b^{2}}{3 c^{2} + 4 d^{2}} = \frac{3 a^{2} - 4 b^{2}}{3 c^{2} - 4 d^{2}}

\frac{a}{b} = \frac{c}{d}

\frac{3 a - 5 b}{3 a + 5 b} = \frac{3 c - 5 d}{3 c + 5 d}

3 a - 4 b + 3 c

- 4 a + 5 b - 6 c

4 a - 7 b + 6 c

△ =

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + b + c 3 a & 4 a + 3 b & 5 a + 4 b + 3 c 6 a & 9 a + 6 b & 11 a + 9 b + 6 c \end{matrix} ∣ ∣ ∣ ∣

b = ω

c = ω^{2}

△

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