solve the following equation by factorization method: a square x square - 2A cube x + X raise to power 4 + c square is equal to zero
Answers
Answer:
Identify the given information in the problem:
−
x
2
+
16
x
−
61
=
0
−x2+16x−61=0
On factoring out -1 from
−
x
2
+
16
x
−
61
=
0
−x2+16x−61=0, we have:
−
1
(
x
2
−
16
x
+
61
)
=
0
⇒
x
2
−
16
x
+
61
=
0
−1(x2−16x+61)=0⇒x2−16x+61=0
On adding and subtracting the square of
16
2
162 into the above relation, we have:
x
2
−
16
x
+
61
+
(
16
2
)
2
−
(
16
2
)
2
=
0
⇒
x
2
−
16
x
+
(
16
2
)
2
+
61
−
(
16
2
)
2
=
0
⇒
(
x
−
16
2
)
2
+
61
−
(
16
2
)
2
=
0
(
∵
x
2
−
16
x
+
(
16
2
)
2
=
(
x
−
16
2
)
2
)
⇒
(
x
−
16
2
)
2
+
61
−
64
=
0
⇒
(
x
−
16
2
)
2
−
3
=
0
⇒
(
x
−
8
)
2
−
3
=
0
⇒
(
x
−
8
)
2
=
3
⇒
x
−
8
=
±
√
3
x2−16x+61+(162)2−(162)2=0⇒x2−16x+(162)2+61−(162)2=0⇒(x−162)2+61−(162)2=0(∵x2−16x+(162)2=(x−162)2)⇒(x−162)2+61−64=0⇒(x−162)2−3=0⇒(x−8)2−3=0⇒(x−8)2=3⇒x−8=±3
Thus,
x
−
8
=
+
√
3
(
On taking the positive sign in
x
−
8
=
±
√
3
)
⇒
x
=
8
+
√
3
x−8=+3( On taking the positive sign in x−8=±3)⇒x=8+3
And,
x
−
8
=
−
√
3
(
On taking the negative sign in
x
−
8
=
±
√
3
)
⇒
x
=
−
√
3
+
8
⇒
x
=
8
−
√
3