Question

1) a) Factorize: G(x) = (x+5)2 – 3x(x+5).

b) Solve G(x) = 0.
2) In the adjacent figure ABCD is a square:
a) Express the area of the square and the area
of triangle AEB in terms of x.
b) Calculate x so that the area of the square is equal
to 6 times the area of triangle AEB.​

Answer 1

In bold.

Explanation:

a. (x+5)^2 – 3x(x+5) x+5 is common

= (x + 5)(x + 5 - 3x)

= (x + 5)(5 - 2x)

b. (x + 5)(5 - 2x) = 0

x = -5, 2.5.

2a. Area of the square = (x + 5)^2

Area of triangle AEB

= 1/2 * base * height

I am assuming that H is the centre of AB , so

Area = x*x

= x^2.

2b

6x^2 = (x + 5)^2

6x^2 = x^2 + 10x + 25

5x^2 - 10x - 25 = 0

x^2 - 2x - 5 = 0

x = [-(-2) +/- sqrt(2^2 - 4*1*-5)] / 2

x = -1.45, 3.45.

(we ignore the negative).