Maths F5

1 Ley y = 3^x

9^x = 18(3^x) - 72

y^2 - 18y + 72 = 0

(y - 12)(y - 6) = 0

y = 6 or y = 12

So, 3^x = 6 or e^x = 12

x = log6/log3 or log12/log3

2 (x^2 - 2x)^2 + 2 x^2 = 4x +15

(x^2 - 2x)^2 = -2x^2 + 4x +15

Let y = x^2 - 2x

y^2 = -2y + 15

y^2 + 2y - 15 = 0

(y + 5)(y - 3) = 0

y = 3 or y = -5

x^2 - 2x = 3 or x^2 - 2x = -5 (reject)

(x - 3)(x + 1) = 0

x = -1 or x = 3