Question

Plzzzz solve the 2nd question (ii) asap.

Answer 1

1) perimeter of triangle is 24
let the base x
length of congruent side is =2x-13

ATQ
$(2x - 13) + (2x - 13) + x = 24 \\ 4x - 26 + x = 24 \\ 5x = 24 + 26 \\ 5x = 50 \\ x = 10$
length of the base is 10
length of congruent side is =2x-13
=20-13
=7
2) sum of root
${x}^{2} - 4x + 1 \\ a {x}^{2} + bx + c\\ \alpha + \beta = - \frac{b}{a} = - \frac{4}{1} \\ = - 4$
product of root
$\alpha \beta = \frac{c}{a} = \frac{1}{1} \\ = 1$
i)
${ \alpha }^{2} + { \beta }^{2} \\ {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ {( - 4)}^{2} - (2 \times 1) \\ 16 - 2 \\ { \alpha }^{2} + { \beta }^{2} = 14$
ii)
$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } \\ = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } \\ = \frac{14}{1} \\ = 14$