If x^{2}+x=5,then find the value of (x+3)^{3} | vedclass

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(D) Let $a = x+3$. We need to find the value of $a^{3} + \frac{1}{a^{3}}$.Given $x^{2} + x = 5$,we can write $x^{2} = 5 - x$.Now,consider $a = x+3$. T

Vedclass · Accepted Answer

$110$

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(D) Let $a = x+3$. We need to find the value of $a^{3} + \frac{1}{a^{3}}$.Given $x^{2} + x = 5$,we can write $x^{2} = 5 - x$.Now,consider $a = x+3$. Then $x = a - 3$.Substitute $x = a - 3$ into the given equation $x^{2} + x = 5$:$(a - 3)^{2} + (a - 3) = 5$$(a^{2} - 6a + 9) + a - 3 = 5$$a^{2} - 5a + 6 = 5$$a^{2} - 5a + 1 = 0$Divide the entire equation by $a$ (since $a 
eq 0$):$a - 5 + \frac{1}{a} = 0$$a + \frac{1}{a} = 5$We know that $a^{3} + \frac{1}{a^{3}} = (a + \frac{1}{a})^{3} - 3(a + \frac{1}{a})$.Substituting the value $a + \frac{1}{a} = 5$:$a^{3} + \frac{1}{a^{3}} = 5^{3} - 3(5) = 125 - 15 = 110$.

If $x^{2}+x=5$,then find the value of $(x+3)^{3}+\frac{1}{(x+3)^{3}}$.

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