If 3x – 2y = 5 and xy = 6, find the value of (27x³ - 8y³).

Given, 3x – 2y = 5 xy = 6 Using identity : (a - b)3 = a3 - b3 - 3ab(a - b) ⇒ (3x – 2y)3 = [(3x)3 - (2y)3 - 3 × 3x × 2y × (3x - 2y)] ⇒ (5)3 = 27x3 - 8y3 - 18xy × (5) ⇒ 125 = 27x3 - 8y3 - 90xy ⇒ 125 = 27x3 - 8y3 - 90(6) ⇒ 27x3 - 8y3 = 125 + 540 ⇒ 27x3 - 8y3 = 665 Hence, 27x3 - 8y3 = 665.

Mathematics

If 3x – 2y = 5 and xy = 6, find the value of $27x^3 - 8y^3$ .

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Answer

Given,

3x – 2y = 5

xy = 6

Using identity :

(a - b)³ = a³ - b³ - 3ab(a - b)

⇒ (3x – 2y)³ = [(3x)³ - (2y)³ - 3 × 3x × 2y × (3x - 2y)]

⇒ (5)³ = 27x³ - 8y³ - 18xy × (5)

⇒ 125 = 27x³ - 8y³ - 90xy

⇒ 125 = 27x³ - 8y³ - 90(6)

⇒ 27x³ - 8y³ = 125 + 540

⇒ 27x³ - 8y³ = 665

Hence, 27x³ - 8y³ = 665.

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Mathematics

If 3x – 2y = 5 and xy = 6, find the value of $27x^3 - 8y^3$ .

Expansions

Answer

Related Questions

Expand:
(i) (3a + 5b)³
(ii) (2p - 3q)³
(iii) $\Big(2x + \dfrac{1}{3x}\Big)^3$
(iv) (3ab - 2c)³
(v) $\Big(3a - \dfrac{1}{a}\Big)^3$
(vi) $\Big(\dfrac{1}{2}x - \dfrac{2}{3}y\Big)^3$

If 4a + 3b = 10 and ab = 2, find the value of $64a^3 + 27b^3$ .

If a + 3b = 6, show that $a^3 + 27b^3 + 54ab = 216$ .

If a + 2b + 3c = 0, show that a³ + 8b³ + 27c³ = 18abc.

Mathematics

If 3x – 2y = 5 and xy = 6, find the value of 27x3−8y327x^3 - 8y^327x3−8y3.

Expansions

Answer

Related Questions

Expand:(i) (3a + 5b)3(ii) (2p - 3q)3(iii) (2x+13x)3\Big(2x + \dfrac{1}{3x}\Big)^3(2x+3x1​)3(iv) (3ab - 2c)3(v) (3a−1a)3\Big(3a - \dfrac{1}{a}\Big)^3(3a−a1​)3(vi) (12x−23y)3\Big(\dfrac{1}{2}x - \dfrac{2}{3}y\Big)^3(21​x−32​y)3

If 4a + 3b = 10 and ab = 2, find the value of 64a3+27b364a^3 + 27b^364a3+27b3.

If a + 3b = 6, show that a3+27b3+54ab=216a^3 + 27b^3 + 54ab = 216a3+27b3+54ab=216.

If a + 2b + 3c = 0, show that a3 + 8b3 + 27c3 = 18abc.

If 3x – 2y = 5 and xy = 6, find the value of $27x^3 - 8y^3$ .

Expand:
(i) (3a + 5b)³
(ii) (2p - 3q)³
(iii) $\Big(2x + \dfrac{1}{3x}\Big)^3$
(iv) (3ab - 2c)³
(v) $\Big(3a - \dfrac{1}{a}\Big)^3$
(vi) $\Big(\dfrac{1}{2}x - \dfrac{2}{3}y\Big)^3$

If 4a + 3b = 10 and ab = 2, find the value of $64a^3 + 27b^3$ .

If a + 3b = 6, show that $a^3 + 27b^3 + 54ab = 216$ .

If a + 2b + 3c = 0, show that a³ + 8b³ + 27c³ = 18abc.