Question

If a=3+2 root 2 find a^4+1/a^4

Answer 1

$a = 3 + 2 \sqrt{2 } \\ {a}^{4 } + 1 \div {a}^{4 } = .... \\ =( a { }^{2} + 1 \div {a}^{2} ) {}^{2} - 2 \\ =( (a + 1 \div a) {}^{2} - 2 ) {}^{2} - 2 \\ =( (3 + 2 \sqrt{2 } + 3 - 2 \sqrt{2} ) {}^{2} - 2) {}^{2} - 2 \\ = ( 36 - 2) {}^{2} - 2 \\ = 34 {}^{2} - 2 \\ = 1156 - 2 \\ = 1154$
I think this would help you