(a+b)²x²-4abx-(a-b)² FIND ROOTS
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Answer:
(x - 1)
[x + (a - b)²/(a + b)²]
Step-by-step explanation:
(a + b)²x² - 4abx - (a - b)² = 0
⇒ x² - 4abx/(a + b)² - (a - b)²/(a + b)² = 0
⇒ x² - 4ab/(a + b)²x - [(a - b)/(a + b)]² = 0
⇒ x² - 4ab/(a + b)²x + 4a²b²/(a + b)⁴ = [(a - b)/(a + b)]² + 4a²b²/(a + b)⁴
⇒ [x - 2ab/(a + b)²]² = {(a - b)²(a + b)² + 4a²b²}/(a + b)⁴
⇒ [x - 2ab/(a + b)²]² = {(a² + b²)/(a + b)²]²
Taking square root both sides,
⇒[x - 2ab/(a + b)² ] = ± (a² + b²)/(a + b)²
⇒x = {2ab ± (a² + b²)}/(a + b)²
⇒x = (a + b)²/(a + b)² , -[(a -b)/(a + b)]²
⇒x = 1 , -(a - b)²/(a + b)²
Hence, factors are (x - 1) and [x + (a - b)²/(a + b)² ].
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