Question

32. If 3x- 4y = 5 andxy = 5, find the value of (3x + 4y)²​

Answer 1

$\rm{(3x + 4y)^2}$

• Apply Algebraic Identity : $\rm{(a-b)^2=a^2+b^2-2ab}$

$\to\rm{(3x-4y)^2=3x^2+4y^2-2\times 3x\times 4y}$

• Substitute 3x - 4y = 5

$\to\rm{5^2=3x^2+4y^2-24xy}$

• Substitute xy= 5

$\to\rm{5^2=3x^2+4y^2-24\times 5}$

$\to\rm{5^2=3x^2+4y^2-120}$

• We know 5² = 25

$\to\rm{25=3x^2+4y^2-120}$

• Adding 120 To Both Sides

$\to\rm{25+120=3x^2+4y^2-120+120}$

$\to\rm{145=3x^2+4y^2}\:\:\: \bf{........1}$

• Apply Algebraic Identity : $\rm{(a+b)^2=a^2+b^2+2ab}$

$\to\rm{(3x+4y)^2=3x^2+4y^2+2\times 3x\times 4y}$

• Substitute xy= 5

$\to\rm{(3x+4y)^2=3x^2+4y^2+24\times5}$

$\to\rm{(3x+4y)^2=3x^2+4y^2+120}$

• Substitute The Value of $\rm{3x^2+4y^2}$ from (1)

$\to\rm{(3x+4y)^2=145+120}$

$\to\rm{(3x+4y)^2=165}$