Question

if the sum of 4 numbers in A.p is 24 and sum of their squares is 164 find the numbers​

Answer 1

Step-by-step explanation:

hope to may help u..........

Answer 2

Answer:

$3,5,7,9.$

Step-by-step explanation:

$(a-3d)+(a-d)+(a+d)+(a+3d)\;=\;24$

$4a\;=\;24$

∴ $a\;=\;6$

$(a-3d)^2+(a-d)^2+(a+d)^2+(a+3d)\;=\;164$

$2(a^2+9d^2)+2(a^2+d^2)\;=\;164$

$a^2+5d^2\;=\;41\;=\;36+5d^2\;=\;41\;=\;d\;=\;$ ± $1$

∴ Required numbers are $3,5,7,9.$