If x2 - √7x + 1 = 0, then what is the value of x5 + ?
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 19√7
x2 - √7x + 1 = 0
On dividing by x on both sides we get,
⇒ x - √7 + 1/x = 0
⇒ x + 1/x = √7.........(1)
on squaring both sides we get,
⇒ x2 + 1/x2 = 7 - 2
⇒ x2 + 1/x2 = 5.........(3)
On cubing both sides in equation 1 we get,
⇒ x3 + 1/x3 + 3(x + 1/x) = 7√7.
⇒ x3 + 1/x3 = 4√7...........(4)
Now lets multiply (3) with (4) we get,
x5 + 1/x5 + x + 1/x= 20√7
x5 + 1/x5 = 20√7 - √7 = 19√7.