3x + 1/x = 4 x³ + 1/27x³ + 5= ??
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Let a=12x—(1)
b=3x—(2)
Given: 2x−13x=4
=>1a−1b=4
=>b−aab=4
=>b−a=4ab—(3)
From (1) and (2), ab=12x∗3x=32—(5)
27x3−18x3=(3x)3−(12x)3=b3−a3=(b−a)3+3ab(b−a)—(6)
From (3) and (5),
27x3−18x3=(4ab)3+3ab(4ab)=64(ab)3+12(ab)2—(7)
From (5) and (7),
27x3−18x3=[64∗(32)3]+[12∗(32)2]
=[64∗278]+[12∗94]=(8∗27)+(3∗9)=216+27=243
Ans: 243
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