3
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3. Solve : 8x2n – 8x2n = 63
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Answered by
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Answer:
Given, 8x
2n
3
−8x
−
2n
3
=63
⇒8x
2n
3
−
8x
2n
3
1
=63
Put x
2n
3
=t, we get
8t−
t
8
=63
⇒8t
2
−8=63t
⇒8t
2
−63t−8=0
⇒8t
2
−64t+t−8=0
⇒8t(t−8)+1(t−8)=0
⇒(8t+1)(t−8)=0
⇒t=−
8
1
,8
⇒x
2n
3
=t
⇒x=t
3
2n
For t=−
8
1
, we have
x=(−
8
1
)
3
2n
=((−
2
1
)
3
)
3
2n
x=(−
2
1
)
2n
=
2
2n
1
For t=8, we have
x=8
3
2n
=((2)
3
)
3
2n
x=2
2n
So, the values of x are
2
2n
1
and 2
2n
.
Step-by-step explanation:
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