If $ \frac{a}{c} = \frac{c}{d} = k $, find the... | JAMB UTME - Mathematics - 1986

Question 1 Report

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

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

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