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}}

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