Dont mess with k.. ok!!
If k = 2 3 + 1 Then find the value of 4 k 3 + 2 k 2 - 8k + 7
The answer is 10.
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2 solutions
forgot to divide by 4 for the 2k^2 just couldn't see where I was going wrong!
We have k = 2 √ 3 + 1 ⇒ 2 k − 1 = √ 3 Squaring & solving, we get ⇒ 2 k 2 − 2 k − 1 = 0 Now dividing the required expression 4 k 3 + 2 k 2 − 8 k + 7 by 2 k 2 − 2 k − 1 we get 4 k 3 + 2 k 2 − 8 k + 7 = ( 2 k 2 − 2 k − 1 ) ( 2 k + 3 ) + 1 0 ⇒ 4 k 3 + 2 k 2 − 8 k + 7 = 0 + 1 0 = 1 0
k=½(√3+1) k² = 1+½√3 => 2k² = 2+√3 k³ = k.k² = ¼(5+3√3) => 4k³ = 5+3√3 =>....... 4k³ = 5+3√3 +2k² = 2+√3 -8k = -4√3 - 4 +7 = +7 ---------------------- .....= 10