Question

If 24 (3 x square -y square small) = 37 x y find X : y

Answer 1

(24)

Given:

• 24(3x² -y²)=37xy

To Find:

• x:y

Solution:

⟼ 24(3x² -y²)=37xy

⟼ 72x² -24y²-37xy=0

⟼ 72x² -37xy-24y²=0

⟼ 72x² -64xy+27xy-24y²=0

⟼ 8x(9x-8y)+3y(9x-8y)=0

⟼ (8x+3y)(9x-8y)=0

⟼ 8x+3y=0  ,  9x-8y=0

⟼ 8x= -3y  ,  9x=8y

$\longrightarrow\sf{\dfrac{x}{y}=\dfrac{-3}{8}\:\:\:,\:\:\dfrac{x}{y}=\dfrac{8}{9}}$

$\longrightarrow\sf\pink{\dfrac{x}{y}=\dfrac{-3}{8},\dfrac{8}{9}}$

Hence, x:y is -3:8 or 8:9.

$\rule{200}{2}$

(25)

Given:

• (3x+5y):(2x-y)=(12x-y):(5x-3y)

To Find:

• x:y

Solution:

$\longrightarrow\sf{\dfrac{3x+5y}{2x-y}=\dfrac{12x-y}{5x-3y}}$

$\longrightarrow\sf{(3x+5y)(5x-3y)=(12x-y)(2x-y)}$

$\longrightarrow\sf{15x^{2} -9xy+25xy-15y^{2}=24x^{2} -12xy-2xy+y^{2}}$

$\longrightarrow\sf{15x^{2} -9xy+25xy-15y^{2}-24x^{2} +12xy+2xy-y^{2}=0}$

$\longrightarrow\sf{-9x^{2}+30xy-16y^{2}=0}$

$\longrightarrow\sf{-1(9x^{2}-30xy+16y^{2})=0}$

$\longrightarrow\sf{9x^{2}-30xy+16y^{2}=0}$

$\longrightarrow\sf{9x^{2}-6xy-24xy+16y^{2}=0}$

$\longrightarrow\sf{3x(3x-2y)-8y(3x-2y)=0}$

$\longrightarrow\sf{(3x-8y)(3x-2y)=0}$

$\longrightarrow\sf{3x=8y\:\:\:,\:\:\:3x=2y}$

$\longrightarrow\sf{\dfrac{x}{y}=\dfrac{8}{3}\:\:\:,\:\:\dfrac{x}{y}=\dfrac{2}{3}}$

$\longrightarrow\sf\purple{\dfrac{x}{y}=\dfrac{8}{3},\dfrac{2}{3}}$

Hence, x:y is 8:3 or 2:3.