Question

find value find value find value

Answer 1

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Answer 2

Find the value:

Step-by-step explanation:

$\ Given \ value: \\\\x^3+ \frac{1}{x^3} \ = 110\\\\\ Find: \\\\x+\frac{1}{x} = ?\\\\ \ Solution: \\\\\ formula: \\\\(a+b)^3 =a^3+b^3+3ab(a+b) \\\\(x+\frac{1}{x})^3 =x^3+(\frac{1}{x})^3 +3 \cdot x^3\cdot\frac{1}{x^3}(x+\frac{1}{x})$

$\therefore x^3+\frac{1}{x^3} =110\\\\(x+\frac{1}{x})^3 =x^3+\frac{1}{x^3} +3(x+\frac{1}{x})\\\\(x+\frac{1}{x})^3 =110+3(x+\frac{1}{x})\\\\(x+\frac{1}{x})^3-3(x+\frac{1}{x}) =110 \\\\ \ let \ x+\frac{1}{x} =t\\\\\ so, \\\\t^3-3t=110......(1)\\\\\ by \ hit \ and \ tarial \ method \ we \ assume \ t \ = 5\\\\ \ put the \ value \ of \ t \ in \ equation (1) . \\\\5^3-3\times 5\ =110 \\\\125-15\ = \ 110 \\\\110 =110 \\\\ \ So, \ x+\frac{1}{x} = 5$

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