Find the value of a and b when a+b = -5, ab = -24

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Step-by-step explanation:

Given the 2 equations

a + b = - 5 → (1)

ab = - 24 → (2)

Rearranging (1) expressing a in terms of b, that is

a = - 5 - b → (3)

Substitute a = - 5 - b into (2)

b(- 5 - b) = - 24 ← distribute left side

- 5b - b² = - 24 ( subtract - 5b - b² from both sides )

0 = b² + 5b - 24 ← in standard form

0 = (b + 8)(b - 3) ← in factored form

Equate each factor to zero and solve for b

b + 8 = 0 ⇒ b = - 8

b - 3 = 0 ⇒ b = 3

Substitute these values into (3) for corresponding values of a

b = - 8 : a = - 5 - (- 8) = - 5 + 8 = 3

b = 3 : a = - 5 - 3 = - 8

Thus

a = 3, b= - 8 or a = - 8, b = 3

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

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