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If x=(sqrt(3)+1)/2, find the value of 4x...

If `x=(sqrt(3)+1)/2,` find the value of `4x^3+2x^2-8x+7.`

Text Solution

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`4x^3+2x^2-8x+7.`
`=x[ 4x^2+2x-8]+7`
`=(sqrt(3)+1)/2[4/4xx(sqrt(3)+1)^2+2/2(sqrt(3)+1)-8]+7`
`=(sqrt(3)+1)/2[4+2sqrt3+sqrt3+1-8]+7`
`=(sqrt(3)+1)/2[3sqrt3-3]+7`
`=3/2xx2+7`
`=10`
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