Q. 6

Mark the Correct alternative in the following:The number of real roots of the equation isA. 2B. 1C. 4D. none of these

given (x2+2x)2-(x+1)2-55=0

[(x2 +2x +1) -1] 2 -(x +1)2 -55 =0

(x +1)⁴ -2(x +1)2 +1 -(x +1)2 -55 =0

(x+1)⁴ -3(x +1)2 -54 =0

let (x +1)2= r

r2 -3r -54 =0

r2 -9r +6r -54 =0

r( r -9) +6(r -9) =0

r = -6 , 9

but ( x+1)2 ≥ 0 so, (x+1)2 ≠ -6

so, (x +1)2 = 9

x + 1 = ± 3

x = -1 ±3

x = -4, and 2 .

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