SSC GD Constable 2012 · Question 62 of 95
x2 − 3x + 1=0 Taking 'x' common 1 x(x-3+ x )=0 1 ⇒ x + x =3 → (1) Squaring on both sides 1 1 x2 + x2 + 2 × x × x =9 1 ⇒ x2 + x2 =7 → (2) Cubing equation(1) on both sides 1 1 1 x3 + x3 + 3 × x × x (x + x )=27 1 1 x3 + x3 +3 × 1 × 3=27(∵ x + x =3) 1 x3 + x3 =27-9=18 → (3) Squaring equation(2) on both sides 1 1 x4 + x4 + 2 × x2 × x2 =49 1 x4 + x4 =47 → (4) Multiplying equation(1) and equation(4) 1 1 (27) 1 1 (x4 + x4 )(x + x )=47 × 3 1 1 x5 + x5 + x3 + x3 =47 × 3=141 1 1 x5 + x5 + 18=141(∵ x3 + x3 ) 1 ∴ x5 + x5 =123
Source: Solved SSC GD 2012 Shift 1 Paper with Solutions — Testbook · reliable-secondary
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