If y =root +2 +root −2 / root +2− root −2, prove that b^2 – ay + b = 0
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Answer:
formula,
(a+b+c)
2
=a
2
+b
2
+c
2
+2(ab+bc+ca)
Given,
xyz
1
(x
2
+y
2
+z
2
)+2(
x
1
+
y
1
+
z
1
)
=
yz
x
+
xz
y
+
yx
z
+2(
x
1
+
y
1
+
z
1
)
comparing the above equation with formula, we get,
a
2
=
yz
x
⇒a=
yz
x
similarly
b
2
=
xz
y
⇒b=
xz
y
and
c
2
=
xy
z
⇒c=
yx
z
∴(
yz
x
+
xz
y
+
yx
z
)
2
=
xyz
1
(x
2
+y
2
+z
2
)+2(
x
1
+
y
1
+
z
1
)
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