Question

lets try to prove 27 x^3 + 1/8x^3=189 if 2x+1/3x= 4​

Answer 1

$\huge\red{Answer}$→

The proof is given below

$\huge\green{Step-by-step\;explanation}$→

We are given that

$2x+\frac{1}{3x} =4 \; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ ...(i)$

We are to prove the following :

$27x^{3} +\frac{1}{8x^{3} } =189$

We will be using the following factorization formula :

$(a+b)^{3} = a^{3} +b^{3} +3ab(a+b)$

We have from equation (i) that

Multiplying by on  both sides we get

       ⇒( 3 / 2 ) × ( 2x + 1 / 3x ) = 4 × ( 3 / 2 )  

        ⇒ 3x + 1 / 2x = 6

Taking cube on both sides we get

        ⇒( 3x + 1 / 2x )³ = 6³

Using formula (a + b)³ = a³ + b³ + 3ab(a+b) we get

    ⇒27x³ + 1/8x³ + 3×( 3x )×( 1/2x )×( 3x + 1 / 2x) = 216

Putting "3x + 1 / 2x = 6" we get

    ⇒27x³ + 1/8x³ + 3×3×(1/2 )×6 = 216

    ⇒27x³ + 1/8x³ + 3×3×3 = 216

    ⇒27x³ + 1/8x³ + 27 = 216

Hence proved.

$\bold\pink{@alluringbabe}$