If displaystyle a-2-3a-1-0 the value of displaystyle a-2-frac-1-a-2-1318113

Question

Toppr Admin · Accepted Answer

A2-x2212-3a-x2212-1-0-gt-a2-x2212-1-3a-gt-a-x2212-1a-3Squaring both sides-gt-a-x2212-1a-2-32-gt-a2-1a2-x2212-2-a-1a-9-gt-a2-1a2-9-2-xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0- -xA0-11

If $a^{2} - 3 a - 1 = 0$ find the value of $a^{2} + \frac{1}{a^{2}}$ .
$13$
$18$
$11$
$3$

$a^{2} - 3 a - 1 = 0$
$=> a^{2} - 1 = 3 a$
$=> a - \frac{1}{a} = 3$
Squaring both sides,
$=> (a - \frac{1}{a})^{2} = 3^{2}$
$=> a^{2} + {\frac{1}{a}}^{2} - 2 (a) (\frac{1}{a}) = 9$
$=> a^{2} + {\frac{1}{a}}^{2} = 9 + 2$
$= 11$

If a2−3a−1=0 find the value of a2+1a2.1318113

a2−3a−1=0=>a2−1=3a=>a−1a=3Squaring both sides,=>(a−1a)2=32=>a2+1a2−2(a)(1a)=9=>a2+1a2=9+2 =11

If $a^{2} - 3 a - 1 = 0$ find the value of $a^{2} + \frac{1}{a^{2}}$ .
$13$
$18$
$11$
$3$

$a^{2} - 3 a - 1 = 0$
$=> a^{2} - 1 = 3 a$
$=> a - \frac{1}{a} = 3$
Squaring both sides,
$=> (a - \frac{1}{a})^{2} = 3^{2}$
$=> a^{2} + {\frac{1}{a}}^{2} - 2 (a) (\frac{1}{a}) = 9$
$=> a^{2} + {\frac{1}{a}}^{2} = 9 + 2$
$= 11$