Question

1 If (4x2 + (x2) = 4., find the values of: () (2x - 3) (1) (8x3 - 27x3​

Answer 1

Step-by-step explanation:

Let a=12x(E01)

b=3x(E02)

Given: 2x−13x=4⟹1a−1b=4⟹b−aab=4

⟹b−a=4ab(E03)

From (E01) and (E02) :

ab=12x⋅3x=32(E04)

27x3−18x3=(3x)3−(12x)3

⟹b3−a3=(b−a)3+3ab(b−a)(E05)

From (E03), (E04) and (E05) :

27x3−18x3=(4ab)3+3ab(4ab)

⟹27x3−18x3=64(ab)3+12(ab)2(E06)

From (E04) and (E06) :

27x3−18x3=[64⋅(32)3]+[12⋅(32)2]

=[64⋅278]+[12⋅94]

=(8×27)+(3×9)=216+27=243

Ans: 243