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Lets try to prove 27 x^3 + 1/8x^3=189 if 2x+1/3x= 4 |
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Answer» oof is given below→ We are given thatWe are to prove the following :We will be using the following factorization formula :We have from equation (i) thatMultiplying by on both SIDES we get ⇒( 3 / 2 ) × ( 2X + 1 / 3x ) = 4 × ( 3 / 2 ) ⇒ 3x + 1 / 2x = 6Taking 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. |
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