Question

If3x–2y=11 and xy=12, find the value of 27x^3–8y^3 .

Answer 1

Answer:

3707

Step-by-step explanation:

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Answer 2

ANSWER:

• Value of the above expression is 3707.

GIVEN:

• 3x-2y = 11....(i)
• xy = 12 ....(ii)

TO FIND:

• Value of (27x³-8y³)

SOLUTION:

=> 3x-2y = 11

Squaring both sides we get;

=> (3x-2y)² = (11)²

=> 9x²+4y²-12xy = 121

Putting xy = 12 from (ii).

=> 9x²+4y²-12(12) = 121

=> 9x²+4y² = 121+144

=> 9x²+4y² = 265

Formula:

• x³-y³ = (x-y)(x²+y²+xy)

= (27x³-8y³)

= (3x)³-(2y)³

= (3x-2y)(9x²+4y²+6xy)

Putting the values:

= 11[265+6(12)]

= 11(265+72]

= 11(337)

= 3707

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab