Question

Hi May I know how to solve this question with step by step explanation please

Answer 1

Answer:

a = 1, b = - 2

Step-by-step explanation:

The points that lie on the curve and straight line satisfy the corresponding equations.

Substitute the points into their corresponding equations, that is

(1, - 1 ) → - a = 1² + b = 1 + b ( multiply both sides by - 1 )

a = - 1 - b → (1)

(3, 3 ) → $\frac{-3b}{2}$ = $\frac{3}{a}$ ( cross- multiply )

- 3ab = 6 ( divide both sides by - 3 )

ab = - 2 → (2)

Substitute a = - 1 - b into (2)

(- 1 - b)b = - 2 , distribute left side

- b - b² = - 2 ( multiply through by - 1 )

b² + b = 2 ( subtract 2 from both sides )

b² + b - 2 = 0 ← in standard form

(b + 2)(b - 1) = 0 ← in factored form

Equate each factor to zero and solve for b

b + 2 = 0 ⇒ b = - 2

b - 1 = 0 ⇒ b = 1

Substitute these values into (1) for corresponding values of a

b = - 2 : a = - 1 - (- 2) = - 1 + 2 = 1

b = 1 : a = - 1 - 1 = - 2

Thus a = - 2, b = 1 or a = 1, b = - 2

Given that a > b then a = 1, b = - 2