if x = 7+4√3 and xy =. 1, then find 1/x^2 +1/y^2
Answers
Answered by
1
Answer:
194
Step-by-step explanation:
x=7+4
3
x
1
=
(7+4
3
)(7−4
3
)
7+4
3
[∴(a+b)(a−b)=a
2
−b
2
]
=
(7)
2
−(4
3
)
2
7−4
3
=
49−48
7−4
3
=
1
7−4
3
=7−4
3
Given, xy=1
y
1
=x
y
1
=7+4
3
⇒
x
2
1
+
y
2
1
=(7−4
3
)
2
+(7+4
3
)
2
⇒
x
2
1
+
y
2
1
=(7)
2
+4(
3
)
2
−2×7×4
3
×(7)
2
+(4
3
)
2
+2×7×4
3
⇒
x
2
1
+
y
2
1
=49+48+49+48
⇒
x
2
1
+
y
2
1
=194
Answered by
1
Step-by-step explanation:
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