Question

a aquare + 9/a square = 31 then find the value of a-3/a

Answer 1

given,
${a}^{2} + 9 \div {a }^{2} = 31$
We have to find a-3/a

from given equation ,
${a}^{4 } + 9 \div {a}^{2} = 31$
${a}^{4 } + 9 = 31 {a}^{2}$
${a}^{4 } - 31 {a}^{2} + 9 = 0$

${a}^{2} ( {a }^{2} - 31) + 9 = 0$
${a}^{2} - 31 + 9 = 0$
${a}^{2} = 22$
a=root 22
hence your answer is 19/root22