Given,
[tex]x - \frac{1}{x} = 5[/tex]
Squaring both sides, we get
[tex] = > (x - \frac{1}{x} )^{2} = {(5)}^{2} [/tex]
By using the identity: (a - b)² = a² - 2ab + b², we have:
[tex] = > {x}^{2} - 2(x)( \frac{1}{x} ) + (\frac{1}{x} ) ^{2} = 25 \\ = > {x}^{2} - 2 + \frac{1}{ {x}^{2} } = 25[/tex]
Now, transpose -2 to the right hand side.
[tex] = > {x}^{2} + \frac{1}{ {x}^{2} } = 25 + 2 \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 27[/tex]
Answer:
27
Hope you could understand.
If you have any query, feel free to ask.
Given: {x -(1/x)} = 5
Asked: = {x² + (1/x²)} = ?
Solution:
Given that:
{x - (1/x)} = 5
On squaring both sides then
→ {x - (1/x)}² = (5)²
Now
Compare the LHS with (a-b)², we get
a = x and b = 1/x
Using identity (a -b)² = a² - 2ab + b² , we get
→ {x - (1/x)}² = (5)²
→ x² - 2(x)(1/x) + (1/x)² = 5*5
Multiply the number on RHS.
→ x² - 2(x)(1/x) + (1/x²) = 25
Cancel both “x” on RHS. Because they are in multiple sign.
→ x² - 2 + (1/x²) = 25
Shift the number 2 from LHS to RHS, changing it's sign.
→ x² + (1/x²) = 25 + 2
Add the numbers on RHS.
→ x² + (1/x²) = 27
Therefore, {x² + (1/x²)} = 27
Answer: Hence, the value of {x² + (1/x²)} = 27
Please let me know if you have any other questions.
