Question

If a = (V5 +1)/2, find the value of 4a3 + 2a2 – 8a + 7 step by set​

Answer 1

Given,

a - 1/a = 5——————————————-(1)

Squaring both sides, we get

a² + 1/a² - 2(a)(1/a) = 25,

==> a² + 1/a² = 25+2=27,—————————(2)

Adding 2 to both sides of (2)we get

a² + 1/a² + 2 = 27+2= 29 —————————-(3)

==> [ a + (1/a)]² = 29 ———————————(4)

Taking square root of (4) we get

( a + 1/a ) = ± √29————————————-(5)

Multiplying (1) and (5) we get,

( a -1/a)(a +1/a)= ± 5√29

==> a² - 1/a² = ± 5√29 ———————————(6)

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