If x = 2 + √3 the value of x3 + 3x2 – 27 x + 87 is
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the value of
Putting, x = 2 + √3 in p(x) = x³+ 3x² - 27x + 87
(2 + √3)³ + 3(2 + √3)² - 27(2 + √3) + 87
(2)³ + (√3)³ + 3(2)(√3)(2 + √3) + 3(2 + √3)² - 27(2 + √3) + 87
4 + 3√3 + 6√3( 2 + √3) + 3{(2)²+ (√3)²+2(2)(√3)} - 54 - 27√3 + 87
4 + 3√3 + 12√3 + 54 + 3(4 + 3 + 4√3) - 27√3 + 33
4 + 3√3 + 12√3 + 54 + 12 + 9 + 12√3 - 27√3 + 33
3√3 + 12√3 + 12√3 - 27√3 + 4 + 54 + 12 + 9 + 33
+ 112
112
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Identities used:-
- (a + b)³ = a³ + b³ + 3ab(a + b)
- (a + b)² = a² + b² + 2ab
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