Question

x4+1/x4=623, find the value of x+1/x by taking only the position of x+1/x,x2+1/x2

Answer 1

we can solve the given question by following
i.e. taking the formula a^2+b^2= (a+b)^2-2ab
@sumo2

Answer 2

Answer:

$\big(x^{2}+\frac{1}{x^{2}}\big)=25</p><p>$

$\big(x^+\frac{1}{x}\big)=3\sqrt{3}$

Step-by-step explanation:

$Given \: x^{4}+\frac{1}{x^{4}}=623---(1)$

/* We know the algebraic identity:

a²+b² = (a+b)²-4ab */

$\implies (x^{2})^{2}+\big(\frac{1}{x^{2}}\big)^{2}+2 \times x^{2}\times \frac{1}{x^{2}}\\=623+2$

$\implies \big(x^{2}+\frac{1}{x^{2}}\big)^{2}=625$

$\implies \big(x^{2}+\frac{1}{x^{2}}\big)^{2}=(25)^{2}$

$\implies \big(x^{2}+\frac{1}{x^{2}}\big)=25---(2)</p><p>$

Again,

$\implies \big(x^{2}+\frac{1}{x^{2}}+2\big)=25+2$

$\implies \big(x+\frac{1}{x}\big)^{2}=27$

$\implies \big(x+\frac{1}{x}\big)=3\sqrt{3}$

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