Question

If a2 + 1/a2=23 and a≠0,find the value of a+1/a​

Answer 1

Question:-

a2 + 1/a2=23 and a≠0,find the value of a+1/a

Solution:-

$a−a1=8 \\ </p><p></p><p>Squaring both sides, \\ </p><p></p><p>=(a−a1)2=82 \\ </p><p></p><p>=a2+(a1)2−2(a)(a1)=64 \\ </p><p></p><p>=a2+a21−2=64 \\ </p><p></p><p>=a2+a21=66 \\ </p><p></p><p>Now, \\ </p><p></p><p>(a+a1)2=a2+a21+2(a)(a1) \\ </p><p></p><p>  =66+2 \\ </p><p></p><p> =68 \\ </p><p></p><p>=>a+a1=68 \\ </p><p></p><p>   =±217 \\</p><p></p><p>Now, \\ </p><p></p><p>a2−a21=(a+a1)(a−a1) \\ </p><p>  =±(217)(8) \\ </p><p></p><p>  =±1617 \\ </p><p></p><p>$