if (a+(1/a))=15 find the value of (a^2 +(1/a^2 ))


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Question Number 212327 by MASANJAJJ last updated on 10/Oct/24

$i f (a + \frac{1}{a}) = 15 f i n d t h e v a l u e o f (a^{2} + \frac{1}{a^{2}})$
	Answered by universe last updated on 10/Oct/24

	${(a + \frac{1}{a})}^{2} = 15^{2}$ $a^{2} + \frac{1}{a^{2}} + 2 = 225$ $a^{2} + \frac{1}{a^{2}} = 225 - 2 = 223$
	Answered by mehdee7396 last updated on 10/Oct/24

	${(a + \frac{1}{a})}^{2} = 225 \Rightarrow a^{2} + \frac{1}{a^{2}} = 223 ✓$
	Answered by Rasheed.Sindhi last updated on 10/Oct/24

	$Another way$ $a + \frac{1}{a} = 15; a^{2} + \frac{1}{a^{2}} = ?$ $a + \frac{1}{a} = 15 \Rightarrow a^{2} = 15 a - 1$ $\Rightarrow \frac{1}{a} = 15 - a \Rightarrow \frac{1}{a^{2}} = a^{2} - 30 a + 225$ $= 15 a - 1 - 30 a + 225 = 224 - 15 a$ $a^{2} + \frac{1}{a^{2}} = (15 a - 1) + (224 - 15 a) = 223$
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