Question

Find the values of the numbers m and n that will make (2x + m)2 = 4x2 + nx + 9 true, given
that both m and n are positive numbers.

Answer 1

The values of the numbers m and n that makes the given expression true are 3 and 12 respectively

Solving an equation

From the question, we are to determine the values of the numbers m and n that will make the given expression true

The given expression is

(2x + m)² = 4x² + nx + 9

Opening the bracket on the left hand side,

(2x + m)²

(2x + m)(2x + m)

4x² + 2mx + 2mx + m²

4x² + 4mx + m²

∴ 4x² + 4mx + m² = 4x² + nx + 9

By comparing,

4mx = nx;

Then, 4m = n

and

m² = 9

∴ m = ±√9

m = ±3

Since we are given that both m and n are positive numbers,

∴ m = 3

Substitute the value of m into the equation, 4m = n

4×3 = n

∴ n = 12

Hence, the values of the numbers m and n that makes the given expression true are 3 and 12 respectively

Learn more on Solving an equation here: https://brainly.com/question/11820998

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