If ac a c = cd c d = k, find the value of... | JAMB UTME - Mathematics - 1986

Question 1 Report

If $\frac{a}{c}$ = $\frac{c}{d}$ = k, find the value of $\frac{3 a^{2} - a c + c^{2}}{3 b^{2} - b d + d^{2}}$

3k2

2k - k2

\frac{3 b^{2} k^{2} - b k^{2} d + d k^{2}}{3 b^{2} - b d + d^{2}}

Answer Details

$\frac{a}{c}$ = $\frac{c}{d}$ = k
∴ $\frac{a}{b}$ = bk
$\frac{c}{d}$ = k
∴ c = dk
= $\frac{3 a^{2} - a c + c^{2}}{3 b^{2} - b d + d^{2}}$
= $\frac{3 (b k)^{2} - (b k) (d k) + d k^{2}}{3 b^{2} - b d + a^{2}}$
= $\frac{3 b^{2} k^{2} - b k^{2} d + d k^{2}}{3 b^{2} - b d + d^{2}}$
k = $\frac{3 b^{2} k^{2} - b k^{2} d + d k^{2}}{3 b^{2} - b d + d^{2}}$

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If ac a c = cd c d = k, find the value of 3a2?ac+c23b2?bd+d2

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If ac a c = cd c d = k, find the value of 3a2?ac+c23b2?bd+d2

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