model 3 based on positive and negative exponent Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer:(b)

$x = 3^{1/3}- 3^{-1/3}$

On cubing both sides,

$x^3 = ((3)^{1/3})^3 -((3)^{-1/3})^3 -3×3^{1/3}×3^{-1/3}(3^{1/3}- 3^{-1/3})$

$x^3 = 3 - 3^{ - 1}$ - 3x

$x^3 + 3x = 3 - 1/3$

$x^3 + 3x = {9 -1}/3 = 8/3$

$3x^3$ + 9x = 8

Answer:(b)

$2^{x+4} - 2^{x+2}$ = 3

$2^{x+2}(2^2 - 1)$ = 3

$2^{x+2}$× 3 = 3

$2^{x+2}$ = 1 = 2°

x + 2 = 0 ⇒ x = - 2

Answer:(d)

$3^34 = (3^2)^17 = 9^17$

$2^51 = (2^3)^17 = 8^17$

$7^17 = 7^17$

Clearly, $9^17 > 8^17 > 7^17$

i.e., $3^34 > 2^51 > 7^17$

Answer:(a)

a = 7 - $4√3$

$1/a=1/{7-4√3}$

=$1/{7-4√3}×{7+4√3}/{7+4√3}=7+4√3$

$(√a+1/√a)^2=a+1/a+2$

$=7-4√3+7+4√3+2=16$

$√a+1/√a=4$