Question

find 16a2+ 25b2, if ( 4a + 5b) = 12 and ab = 2​

Answer 1

Answer:

$16a^{2} + 25b^{2} = 64$

Step-by-step explanation:

$(4a + 5b)^{2}$ = $16a^{2} + 25b^{2} + 2(4a)(5b)$

$12^{2} = 16a^{2} + 25b^{2} + 2(4)(5)(ab)$

$144 = 16a^{2} + 25b^{2} + 40(2)$

$144 = 16a^{2} + 25b^{2} + 80$

∴$16a^{2} + 25b^{2} = 144 - 80$

$16a^{2} + 25b^{2} = 64$