If 8K⁶ + 15K³ - 2 = 0, then for positive value of K, find (K + 1/K)² = ?

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28 Jun 2022 Algebra

If 8K⁶ + 15K³ - 2 = 0, then for positive value of K, find (K + 1/K)² = ?

OPtion

1) 4225/64
2) 65/8
3) 125/9
4) 85/4
5) 65/9
6) 45/4
7) 25/2
8) 81/16
9) 25/4
10) None of these

Solution

8K⁶ + 15K³ - 2 = 0
For simplifying & solving, let K³=x, then above equation becomes 8x² + 15x - 2 = 0
8x² + 16x -x - 2 = 0
(8x-1) (x+2) = 0
x=1/8, -2
As we require +ve value of K, so consider x=1/8
.'. K³=1/8 or K=1/2
Hence, (K + 1/K)² = (1/2 + 2)² = 1/4 + 2 + 4 = 25/4
Correct Option 9)

Correct Option: 9 Best Solution (1)

G.S.Kantharao   1 year AGO

let k^3=x
8x^2+15x-2=0
x=1/8 or -2
So k^3 = 1/8=>k=1/2
=(1/2+2)^2
=25/4
so my option is 9👈

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