Question

If x = 3 + √8, then find the value of $x^{2} + 1/x^{2}$

Answer 1

x = 3+ √8

x = 3+ √8x = (3+√8)(3-√8) / (3-√8)

x = 3+ √8x = (3+√8)(3-√8) / (3-√8)x = (9 -8) / (3-√8)

x = 3+ √8x = (3+√8)(3-√8) / (3-√8)x = (9 -8) / (3-√8)x = 1/ (3 -√8)

x = 3+ √8x = (3+√8)(3-√8) / (3-√8)x = (9 -8) / (3-√8)x = 1/ (3 -√8)Or we can write 1/x = (3-√8)

x = 3+ √8x = (3+√8)(3-√8) / (3-√8)x = (9 -8) / (3-√8)x = 1/ (3 -√8)Or we can write 1/x = (3-√8)Put the value and find out

x = 3+ √8x = (3+√8)(3-√8) / (3-√8)x = (9 -8) / (3-√8)x = 1/ (3 -√8)Or we can write 1/x = (3-√8)Put the value and find outx² +(1/x²) = x² + (1/x)²

x = 3+ √8x = (3+√8)(3-√8) / (3-√8)x = (9 -8) / (3-√8)x = 1/ (3 -√8)Or we can write 1/x = (3-√8)Put the value and find outx² +(1/x²) = x² + (1/x)²So x² + 1/ x² = (3 +√8)² + (3 -√8)²

x = 3+ √8x = (3+√8)(3-√8) / (3-√8)x = (9 -8) / (3-√8)x = 1/ (3 -√8)Or we can write 1/x = (3-√8)Put the value and find outx² +(1/x²) = x² + (1/x)²So x² + 1/ x² = (3 +√8)² + (3 -√8)²= 9+6√8+8 + 9–6√8+8

x = 3+ √8x = (3+√8)(3-√8) / (3-√8)x = (9 -8) / (3-√8)x = 1/ (3 -√8)Or we can write 1/x = (3-√8)Put the value and find outx² +(1/x²) = x² + (1/x)²So x² + 1/ x² = (3 +√8)² + (3 -√8)²= 9+6√8+8 + 9–6√8+8= 34. Ans…