Question

The sum of the squares of two numbers is 1088. If one of the numbers is 8, find the other number. Give me the right answer only​

Answer 1

Given :

• The sum of the squares of two numbers is 1088.
• One of the number is 8 .

To Find :

• Other number .

Solution :

$\longmapsto\tt{Let\:other\:number\:be={(b)}^{2}}$

A.T.Q :

$\longmapsto\tt{{(8)}^{2}+{(b)}^{2}=1088}$

$\longmapsto\tt{64+{(b)}^{2}=1088}$

$\longmapsto\tt{{b}^{2}=1088-64}$

$\longmapsto\tt{{b}^{2}=1024}$

$\longmapsto\tt{b=\sqrt{1024}}$

$\longmapsto\tt\bf{b=\pm{32}}$

So , The other number is ±32 .

VERIFICATION :

$\longmapsto\tt{{(8)}^{2}+{(b)}^{2}=1088}$

$\longmapsto\tt{{(8)}^{2}+{(32)}^{2}=1088}$

$\longmapsto\tt{64+1024=1088}$

$\longmapsto\tt\bf{1088=1088}$

HENCE VERIFIED

Answer 2

Given that , The sum of the squares of two numbers is 1088 & other of the number is 8 .

Need To Find : The second number ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that the first number be x .

$\\\\\dag\:\underline {\pmb{ {\frak {\: According \:To\:The \:Given \:Condition\:\::\:}}}}\:$

⠀⠀⠀▪︎⠀The sum of the squares of two numbers is 1088 & other of the number is 8 .

$\\\\ \qquad \dashrightarrow \sf \:\Big\{ First \:No.\:\Big\}^2 \:\:+\:\: \Big\{ \: Other \:No.\:\Big\}^2 \:=\:1088\:\:\\\\\\ \qquad \dashrightarrow \sf \:\Big(\:x\:\Big)^2 \:\:+\:\: \Big( \: 8\:\Big)^2 \:=\:1088\:\:\\\\\\ \qquad \dashrightarrow \sf \:\Big(\:x\:\Big)^2 \:\:+\:\: 64 \:=\:1088\:\:\\\\\\ \qquad \dashrightarrow \sf \:x^2 \:\:+\:\: 64 \:=\:1088\:\:\\\\\\ \qquad \dashrightarrow \sf \:x^2 \:=\:1088\:-\:64\:\\\\\\ \qquad \dashrightarrow \sf \:x^2 \: \:=\:1024\:\:\\\\\\ \qquad \dashrightarrow \sf \:x \: \:=\:\sqrt{\Big(\:1024\:\Big)\:}\:\:\\\\\\ \qquad \dashrightarrow \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:32\:}}}}}\:\bigstar \:$

Therefore,

• First Number is , x = 32 &
• Other Number is = 8 .

$\\ \therefore \:\underline {\sf Hence, \:The \:Required \:No.\:is \:\pmb{\sf 32 \:}\:.}$