Question

If a,b are the zeros of x² + √2x + 8 then, find the value of a¹² + b¹² + 10a⁶b⁶ I just want to check : - )

Answer 1

Answer:

a+b= -√2, ab=8 , now

${a}^{12} + {b}^{12} + 2 {a}^{6} {b}^{6} + 8 {a}^{6} {b}^{6} =$

$( { {a}^{6} + {b}^{6}) }^{2} + 8 {(ab)}^{6} =$

$(( {a}^{3} + {b}^{3} ) {}^{2} - 2( {ab)}^{3} ) {}^{2} + 8 \times {8}^{6} =$

$((( {a + b)}^{3} - 3ab(a + b) ) ^{2} - 2( {8})^{3} ) {}^{2} + 2097152 = ((( - \sqrt{2} ) {}^{3} - 3 \times 8( - \sqrt{2} )) {}^{2} - 2 \times 512 ) {}^{2} + 2097152 = (( - 2 \sqrt{2} + 24 \sqrt{2} ) {}^{2} - 1024) {}^{2} + 2097152 = (968 - 1024) {}^{2} + 2097152 = 3136 + 2097152 = 2100288 \: ans$