If x= 1+ V2+13, prove that:
4- 4x + 4x2 + 16x - 8 = 0
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Answer:
x=3+1−−−−√2(E01)
⟹2x=3–√+1⟹(2x−1)=3–√(E02)
Squaring: (2x−1)2=3⟹4x2−4x+1=3
⟹4x2−4x−2=0(E03)
⟹2x2=2x+1(E04)
Given expression is 4x3+2x2−8x+7
=2x2(2x+1)−8x+7
=(2x+1)2−8x+7
=4x2+4x+1−8x+7
=4x2−4x+8
Substituting value for 4x2−4x=2 from (E03):
=4x2−4x+8=2+8=10
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