Solve for x and y, using cross-multiplication method:
bx/a + ay/b = a^2 + b^2 ; x+y=2ab
Answers
Answer:
hey dear friend here's ur answer :-)
\begin{lgathered}\frac{bx}{a} + \frac{ay}{b} = a ^{2} + b^{2} .......eq(1) \\ x + y = 2ab........eq(2)\end{lgathered}
a
bx
+
b
ay
=a
2
+b
2
.......eq(1)
x+y=2ab........eq(2)
\begin{lgathered}now... \\ \\ from \: eq.(1) \\ \frac{b ^{2} x + a ^{2}y }{ab} = a {}^{2} + b {}^{2} \\ \\ b {}^{2} x+ a ^{2}y = a {}^{3} b + b {}^{3} a \\ \\ b {}^{2} x - b{}^{3} a = a {}^{3} b - a {}^{2} y \\ \\ b {}^{2} (x - ab) = a {}^{2} (ab - y) \\ \\ now \: from \: eq \: (2) \\ \\ b {}^{2} ( \frac{x - x}{2} + \frac{y}{2} ) = a {}^{2} ( \frac{x}{2} + \frac{y - y}{2} ) \\ \\ b {}^{2} ( \frac{x}{2} - \frac{y}{2} ) = a {}^{2} ( \frac{x}{2} - \frac{y}{2} ) \\ \\ b {}^{2} x - b {}^{2} y = a {}^{2} x - a {}^{2}y \\ \\ x(b {}^{2} - a {}^{2} ) = y(b {}^{2} - a {}^{2} ) \\ \\ x = y \\ \\ now \: put \: the \: value \: of \: x \: in \: eq \: (2) \\ x + y = 2ab \\ y + y = 2b \\ 2y = 2ab \\ \\ hope \: it \: helps \: u \:\end{lgathered}
now...
fromeq.(1)
ab
b
2
x+a
2
y
=a
2
+b
2
b
2
x+a
2
y=a
3
b+b
3
a
b
2
x−b
3
a=a
3
b−a
2
y
b
2
(x−ab)=a
2
(ab−y)
nowfromeq(2)
b
2
(
2
x−x
+
2
y
)=a
2
(
2
x
+
2
y−y
)
b
2
(
2
x
−
2
y
)=a
2
(
2
x
−
2
y
)
b
2
x−b
2
y=a
2
x−a
2
y
x(b
2
−a
2
)=y(b
2
−a
2
)
x=y
nowputthevalueofxineq(2)
x+y=2ab
y+y=2b
2y=2ab
hopeithelpsu