Question

if (6x + 3y)² = 576 and xy = 6, find the value of 36x² + 9y²​

Answer 1

ANSWER:

• The value of 36x² + 9y² = 360

GIVEN:

• (6x+3y)² = 576
• xy = 6

TO FIND:

• 36x²+9y²

SOLUTION:

=>(6x+3y)² = 576

=> (6x)² + (3y)² +2*(6x)*(3y) = 576

=> 36x² + 9y² +36xy = 576

• Putting xy = 6

=> 36x² + 9y²+(36*6)= 576

=> 36x² + 9y² +216 = 576

=> 36x² + 9y² = 576-216

=> 36x² +9y² = 360

NOTE:

some important formulas:

• (a+b)² = a²+b²+2ab
• (a-b)² = a²+b²-2ab
• (a+b)³ = a³+b³+3ab(a+b)
• (a-b)³ = a³-b³-3ab(a-b)
• (a+b)² = (a-b)²+4ab