let a,b,c be non zero integers such that a/c=a^2+b^2/c^2+b^2 and a is not equal to c, then factorise a^2+b^2+c^2
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Answer:
Given (a+b+c)=0
& q=a
2
+b
2
+c
2
& r=a
4
+b
4
+c
4
We know,
⇒(a+b+c)
2
=a
2
+b
2
+c
2
+2(ab+bc+ca)
Therefore 0
2
=q+2(ab+bc+ca)
⇒ab+bc+ca=
2
−q
⟶(1)
Now, (a
2
+b
2
+c
2
)
2
=a
4
+b
4
+c
4
+2(a
2
b
2
+b
2
c
2
+c
2
a
2
) (all squared )
⇒q
2
=r+2 ( some positive number )
⇒(ab+bc+ca)
2
=a
2
b
2
+b
2
c
2
+c
2
a
2
+2(ab
2
c+a
2
bc+abc
2
)
⇒
4
q
2
−2=a
2
b
2
+b
2
c
2
+c
2
a
2
∴a
2
b
2
+b
2
c
2
+c
2
a
2
<
4
q
2
∴q
2
<r+2(
4
q
2
)
⇒q
2
<r+
2
q
2
⇒
2
q
2
<r
⇒q
2
<2r
Hence, the answer is q
2
<2r.
Step-by-step explanation:
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