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If `x=1/(2-sqrt(3)),`find the value of `x^3-2x^2-7x+5`A. `1`B. `2`C. `3`D. `4` |
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Answer» Correct Answer - C If `x = (1)/(2-sqrt(3))`, then the ………….. We have `x = (1)/(2-sqrt(3)) = (1)/(2-sqrt(3))xx(2+sqrt(3))/(2+sqrt(3)) = (2+sqrt(3))/(2^(2)-(sqrt(3))^(2))` `= (2+sqrt(3))/(4-3) = 2 + sqrt(3)` `implies x - 2 = sqrt(3)` `implies (x-2)^(2) = (sqrt(3))^(2)` `implies x^(2)-4x+4=3` `implies x^(2)-4x+1 = 0` ............... (i) `:. x^(2)-2x^(2)-7x+5` `= x(x^(2)-4x+1)+2(x^(2)-4x+1)+3` `= 3` [using (i)] |
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