Answer:
Correct answer: a) m = 9 ; b) m = 2 and n = 3
Step-by-step explanation:
Given:
a) m x² - 36 = (3 x + 6) (3 x - 6) ⇒ m = ?
b) (m x + n y)² = 4 x² + 12 x y + 9 y² ⇒ m, n = ?
a) m x² - 36 (3 x + 6) (3 x - 6)
The right side of the equation is the difference of the square, so we will present the left side in the same way:
(√m x)² - 6² = (3 x + 6) (3 x - 6)
(√m x + 6) (√m x - 6) = (3 x + 6) (3 x - 6)
√m = 3 /² when we square both sides of the equation we get:
m = 9
b)
(m x + n y)² = 4 x² + 12 x y + 9 y²
The left side of the equation is the complete square of the binomial, so we will present the right side in the same way:
(m x + n y)² = (2 x)² + 2 · 2 x · 3 y + (3 y)² = (2 x + 3 y)²
(m x + n y)² = (2 x + 3 y)² ⇒
m = 2 and n = 3
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