Question

Find the common difference of four numbers in ap whose sum is 0 and product is 9

Answer 1

Answer:

let four numbers be a-3d,a-d,a+d,a+3d

a-3d+a-d+a+d+a+3d=0

0=4a-3d+5d

0=4a+2d

0=2(2a+d)

0=2a+d

d=-2a_____(i)

(a−3d)(a−d)(a+d)(a+3d)=9

$( {a}^{2} -( {3d}^{2} )( {a}^{2} - {d)}^{2} = 9$

${a}^{4} - 10 {a}^{2} {d}^{2} + 9 {d}^{4 } = 9$

$put \: the \: value \: of \: d \:from \: {eq}^{n} - (1)$

${a}^{4} - 10 {a}^{2} {( - 2a)}^{2} + 9 {( - 2a)}^{4} = 9$

hey mate solve after that...