Question:
If x2-4x+3=0, then what is the value of (x3+4x2+7x+24)(x2+2x+3)-1?
If x2-4x+3=0, then what is the value of (x3+4x2+7x+24)(x2+2x+3)-1?
Updated On: Sep 13, 2024
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The Correct Option is C
Solution and Explanation
The correct option is (C): 6.
x2 - 4x + 3 = 0
x2 = 4x - 3...(i)
Now, (x3 + 4x2 + 7x + 24)(x2 + 2x + 3)-1
= (x(4x - 3) + 4x2 + 7x + 24)((4x - 3) + 2x + 3)-1 (from (i))
= (4x2 - 3x + 4x2 + 7x + 24)(6x)-1
= \(\frac{(8x^2 + 4x + 24)}{(6x)}\)
= \((\frac{8(4x-3)+4x + 24)}{(6x)})\) from (i)
= \(\frac{(32x - 24 + 4x + 24)}{(6x)}\)
= 6
x2 - 4x + 3 = 0
x2 = 4x - 3...(i)
Now, (x3 + 4x2 + 7x + 24)(x2 + 2x + 3)-1
= (x(4x - 3) + 4x2 + 7x + 24)((4x - 3) + 2x + 3)-1 (from (i))
= (4x2 - 3x + 4x2 + 7x + 24)(6x)-1
= \(\frac{(8x^2 + 4x + 24)}{(6x)}\)
= \((\frac{8(4x-3)+4x + 24)}{(6x)})\) from (i)
= \(\frac{(32x - 24 + 4x + 24)}{(6x)}\)
= 6
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