ax + by =( a)2 +. ( b)2____ 1.
a + b = 2.a.b __________ 2.
solve this equation with any mehtod.
ans. x = a + b
y = a- b
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Answers
Answer:
Taking x+y=u and x−y=v the given system of equations becomes
au+bu−(a
2
−ab+b
2
)=0
au−bv−(a
2
+ab+b
2
)=0
By cross-multiplication, we have
⇒
b×−(a
2
+ab+b
2
)−(−b)×−(a
2
−ab+b
2
)
u
=
a×−(a
2
+ab+b
2
)+a(a
2
−ab+b
2
)
−v
=
a×−b−a×b
1
⇒
−b(a
2
+ab+b
2
)−−b(a
2
−ab+b
2
)
u
=
−a(a
2
+ab+b
2
)+a(a
2
−ab+b
2
)
−v
=
−ab−ab
1
⇒
−b(a
2
+ab+b
2
+a
2
−ab+b
2
)
u
=
−a(a
2
+ab+b
2
−a
2
+ab−b
2
)
−v
=
−2ab
1
⇒
−2b(a
2
+b
2
)
u
=
−a(2ab)
−v
=
−2ab
1
⇒u=
−2ab
−2b(a
2
+b
2
)
,v=
−2ab
2a
2
b
⇒u=
a
a
2
+b
2
,v=−a
Now, u=
a
a
2
+b
2
⇒x+y=
a
a
2
+b
2
.(i)
and, v=−a⇒x−y=−a ..(ii)
Adding equations (i) and (ii), we get
2x=
a
a
2
+b
2
−a⇒2x=
a
a
2
+b
2
−a
2
⇒2x=
a
b
2
⇒x=
2a
b
2
Substitutiing equation (ii) from equation (i), we get
2y=
a
a
2
+b
2
+a⇒2y=
a
a
2
+b
2
+a
2
⇒y=
2a
2a
2
+b
2
Hence, the solution of the given system of equations is x=
2a
b
2
,y=
2a
2a
2
+b
2
Explanation:
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Answer:
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Explanation:
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