3. What does the child mean by “1 find such pictures in my head”? 6826 ""? Describe any two pictures that the child finds in his head. 4. What are the differences between the waking and sleeping worlds of the child?
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Explanation:
The first equation given,
x-\frac{1}{x}=5x−
x
1
=5 …….. (i)
If we do the cube of equation (i) we get,
\left(x-\frac{1}{x}\right)^{3}=5^{3}(x−
x
1
)
3
=5
3
x^{3}-\left(\frac{1}{x}\right)^{3}-3 \times x \times\left(\frac{1}{x}\right) \times\left(x-\frac{1}{x}\right)=125x
3
−(
x
1
)
3
−3×x×(
x
1
)×(x−
x
1
)=125
x^{3}-\left(\frac{1}{x}\right)^{3}-3\times(x-\frac{1}{x})=125x
3
−(
x
1
)
3
−3×(x−
x
1
)=125
x^{3}-\left(\frac{1}{x}\right)^{3}-3 \times 5=125x
3
−(
x
1
)
3
−3×5=125
Grouping the terms,
x^{3}-\left(\frac{1}{x}\right)^{3}=125+15x
3
−(
x
1
)
3
=125+15
x^{3}-\left(\frac{1}{x}\right)^{3}=140x
3
−(
x
1
)
3
=140
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Answer:
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