If a=2^x , b=2^y and a^2y . b^x =8 , prove that xy =1
Answers
Answered by
0
Answer:
Question
Bookmark
If (x
2
+y
2
)(a
2
+b
2
)=(ax+by)
2
prove that
a
x
=
b
y
Medium
Solution
verified
Verified by Toppr
As we know that
(a+b)
2
=a
2
+b
2
+2ab,(a−b)
2
=a
2
+b
2
−2ab
Given (x
2
+y
2
)(a
2
+b
2
)=(ax+by)
2
x
2
(a
2
+b
2
)+y
2
(a
2
+b
2
)=(ax)
2
+(by)
2
+2(ax)(by)
⟹a
2
x
2
+b
2
x
2
+a
2
y
2
+b
2
y
2
=a
2
x
2
+b
2
y
2
+2abxy
⟹b
2
x
2
+a
2
y
2
=2abxy
⟹(bx)
2
+(ay)
2
−2(bx)(ay)=0
⟹(bx−ay)
2
=0
⟹bx=ay
⟹
a
x
=
b
y
Similar questions