\[\text{If}\quad x+\frac{6}{x}=5, \quad \text{find the value of}\quad x^{2}+\frac{36}{x^{2}}\\[15pt]\text{Click here for Step by step guide detail solution}\\[60pt]\text{Expand the expression}\\\frac{a^{2}}{b}\left(\frac{1}{4}-\frac{b}{a}\right)\\[15pt]\text{click here to find your step by step solved solution}\]
\[\text{To fined the value of}\\[10pt] x^{}+\frac{6}{x}=5\\[15pt]\text{Step 1.}\quad\text{Square the both sides of the expression}\\[15pt]\Rightarrow\qquad\left(x+\frac{6}{x}\right)^{2}=5^{2}\\[15pt]\text{Step 2.}\quad\text{Expand the equation}\\[15pt]\Rightarrow\qquad\left(x+\frac{6}{x}\right)\left(x+\frac{6}{x}\right)=25\\[15pt]\text{Step 3.}\quad\text{Multiply the content of the first parenthesis by the second one}\\[15pt](x\times x)+x\times\frac{6}{x}+\frac{6}{x}{x}+\frac{6}{x}\times\frac{6}{x}\\[15pt]\text{Step 4.}\quad\text{Simplify}\\[15pt]\Rightarrow\qquad x^{2}+6+6+\frac{36}{x^{2}}=25\Rightarrow\\\qquad x^{2}+12+\frac{36}{x^{2}}=25\\[15pt]\Rightarrow\qquad x^{2}+\frac{36}{x^{2}}=25-12\\[15pt]\text{Therefore the value of}\quad x^{2}+\frac{36}{x^{2}}=12\]
Great lesson, keep it up
ReplyDelete