Math Problem Statement

If x + 1/x = 2, find the value of x^2 + 1/x^2.

Solution

The image you uploaded contains the following mathematical problem:

"If x+1x=2x + \frac{1}{x} = 2, find the value of x2+1x2x^2 + \frac{1}{x^2}."

Solution:

Given the equation x+1x=2x + \frac{1}{x} = 2, we need to find the value of x2+1x2x^2 + \frac{1}{x^2}.

  1. Start by squaring both sides of the given equation:

(x+1x)2=22\left( x + \frac{1}{x} \right)^2 = 2^2

  1. Expanding the left-hand side:

x2+2x1x+1x2=4x^2 + 2 \cdot x \cdot \frac{1}{x} + \frac{1}{x^2} = 4

  1. Simplify:

x2+2+1x2=4x^2 + 2 + \frac{1}{x^2} = 4

  1. Subtract 2 from both sides:

x2+1x2=2x^2 + \frac{1}{x^2} = 2

Final Answer:

x2+1x2=2x^2 + \frac{1}{x^2} = 2

Would you like further clarification or details on the solution? Here are some related questions that may interest you:

  1. How do you square binomials?
  2. What happens if x+1x=3x + \frac{1}{x} = 3 instead of 2?
  3. Can this method be applied to other equations of similar form?
  4. How can this result be used in more complex algebraic problems?
  5. What is the importance of simplifying expressions in algebra?

Tip: Always check if there is a pattern or identity that can simplify your calculations in algebra!

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Math Problem Analysis

Mathematical Concepts

Algebra
Squaring Binomials
Equations

Formulas

(a + b)^2 = a^2 + 2ab + b^2

Theorems

Squaring binomial expressions

Suitable Grade Level

Grades 8-10