a) Using componendo and dividendo, solve for x: √2 +√2− √2 −√2− = 3. [3]
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Step-by-step explanation:
ANSWER
1
x
=
a
2
+b
2
−
a
2
−b
2
a
2
+b
2
+
a
2
−b
2
⇒
x−1
x+1
=
a
2
+b
2
+
a
2
−b
2
−
a
2
+b
2
+
a
2
−b
2
a
2
+b
2
+
a
2
−b
2
+
a
2
+b
2
−
a
2
−b
2
⇒
x−1
x+1
=
a
2
−b
2
a
2
+b
2
⇒(
x−1
x+1
)
2
=
a
2
−b
2
a
2
+b
2
⇒(x+1)
2
(a
2
−b
2
)=(a
2
+b
2
)(x−1)
2
⇒(x
2
+1+2x)(a
2
−b
2
)=(x
2
+1−2x)+(a
2
+b
2
)
⇒x
2
a
2
−x
2
b
2
+a
2
−b
2
+2xa
2
−2xb
2
=x
2
a
2
+x
2
b
2
+a
2
+b
2
−2xa
2
−2xb
2
⇒4xa
2
=2x
2
b
2
+2b
2
⇒2xa
2
=x
2
b
2
+b
2
⇒b
2
(x
2
+1)=2xa
2
⇒b
2
=
x
2
+1
2xa
2
.
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