Question

find x in terms of a and b :
9x^2 - 9(a+b)x + [2a^2 + 5ab + 2b^2] = 0​

Answer 1

.Consider, 9x2-9(a+b)x+(2a2+5ab+2b2)=0 
9x2 - 9(a + b)x + (2a2 + 4ab + ab + 2b2) = 0 
9x2 - 9(a + b)x + [2a(a + 2b) + b(a + 2b)] = 0
9x2 - 9(a + b)x + [(a + 2b)(2a + b)] = 0 
9x2 – 3[(a + 2b) + (2a + b)]x + [(a + 2b)(2a + b)] = 0
 9x2 – 3(a + 2b)x - 3(2a + b)x + [(a + 2b)(2a + b)] = 0
3x[3x  – (a + 2b)] - (2a + b)[3x + (a – 2b)] = 0 
[3x  – (a + 2b)][3x - (2a + b)] = 0 
[3x – (a + 2b)] = 0 or [3x - (2a + b)] = 0 
3x  =  (a + 2b) or 3x = (2a + b) x = (a + 2b)/3 or x = (2a + b)/3

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Answer 2

Answer:

x = (a + 2b)/3, x = (2a + b)/3

Step-by-step explanation:

Given Equation is 9x² - 9(a + b)x + [2a² + 5ab + 2b²] = 0

⇒ 9x² - 9(a + b)x + [2a² + 4ab + ab + 2b²] = 0

⇒ 9x² - 9(a + b)x + [(a+2b)(2a + b)] = 0

⇒ 9x² - 3[(2a + b) + (a + 2b)]x + [(a + 2b)(2a + b)] = 0

⇒ 9x² - 3(2a + b)x - 3(a + 2b)x + (a + 2b)(2a + b) = 0

⇒ 3x[3x - (2a + b)] - (a + 2b)[3x - (2a + b)] = 0

⇒ [3x - (a + 2b)][3x - (2a + b)] = 0

⇒ 3x - (a + 2b) = 0, 3x - (2a + b) = 0

⇒ 3x = a + 2b, 3x = 2a + b

⇒ x = (a + 2b)/3, x = (2a + b)/3.

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