JAMB UTME - Mathematics - 1987

x2−y22x2+xy−y2 $\frac{x^2-y^2}{2x^2+xy-y^2}$

2x2+xy−y2=2x2−xy+2xy−y2 $2x^2+xy-y^2=2x^2-xy+2xy-y^2$

= x(2x−y)+y(2x−y) $x(2x-y)+y(2x-y)$

= (x+y)(2x−y) $(x+y)(2x-y)$

x2−y22x2+xy−y2=(x+y)(x−y)(x+y)(2x−y) $\frac{x^2-y^2}{2x^2+xy-y^2}=\frac{(x+y)(x-y)}{(x+y)(2x-y)}$

= x−y2x−y

2415 = 2 x 52 + 4 x 5 + 1 x 5 + 1 x 5o
50 + 20 + 1 = 7110
Convert 7110 to base 8
$\begin{array}{cc}8& 71\\ 8& 8R7\\ 8& 1R0\\ 8& 0R1\end{array}$
= 1078

CF (6) = 5 + 6 + 8 + 10 + 6 + 3
= 38

= 3x < -9

∴ x < -3

$\frac{A_{△PQR}}{A_{TP\left(QRST\right)}}=\frac{\frac{1}{2}\times 2\times h_1}{\frac{1}{2}\times h_2(2+3)}$

$\frac{2}{5}\times \frac{h_1}{h_2}=\frac{2}{5}\times 2$

= $\frac{4}{5}$