Question

if a^2 + b^2 = 8 and ab = 6 find a+ b, a - b, a^2 - b^2 and 3(a + b) ^2 - 2(a - b) ^2​

Answer 1

${a}^{2} + {b}^{2} = 8 \\ ( {a + b})^{2} - 2ab = 8 \\ ( {a + b})^{2} - 12 = 8 \\ ( {a + b})^{2} = 20 \\ \implies a + b = 2 \sqrt{5} ...(1) \\ {a}^{2} + {b}^{2} = 8 \\ ( {a - b})^{2} + 2ab = 8 \\ ( {a - b})^{2} + 12 = 8 \\ ( {a - b})^{2} = -4 \\ \implies a - b = 2i...(2) \\ \\ {a}^{2} - {b}^{2} = (a - b)(a + b) \\ = 2i \times 2 \sqrt{5} \\ = 4 \sqrt{5}i \\ \\ 3( {a + b})^{2} - 2( {a - b})^{2} \\ = 3( {2 \sqrt{5} })^{2} - 2( {2i})^{2} \\ = 3(20) + 2 \times 4 \\ = 60 +8 \\ = 68$

Answer 2

hopefully its helped u :)