Question

the sum of the squares of two positive number is hundred and difference of their square is 28 find the sum of the numbers​

Answer 1

Let the two numbers are x & y

Therefore, x2+y2=100x2+y2=100 ... (i)

x2−Y2=28x2−Y2=28 ... (ii)

Solve eq.(i) and (ii)

x = 8

y = 6

Therefore, x+y=8+6=14

ɦσρε เƭ ɦεℓρร ყσµ 

Answer 2

$\textbf{Let x and y be the two numbers.}$

$\underline{The\: sum\: of\: square\: of \:two \:positive}$ $\underline{number \:(x\:and\:y)\:is\: 100.}$

x² + y² = 100 ....(1)

$\underline{Difference\: of \:their\:(x\:and\:y)\: square\: is\: 28}$

x² - y² = 28 ....(2)

x² = 28 + y² ...(3)

Put value of x² in equation (1)

(28 + y²) + y² = 100

28 + y² + y² = 100

2y² = 100 - 28

2y² = 72

y² = $\dfrac{72}{2}$

y² = 36

y = √36

y = 6

Put value of y in equation (3)

x² = 28 + (6)²

x² = 28 + 36

x² = 64

x = √64

x = 8

$\bold{The\:numbers\:are\::}$

$\bold{x\:=\:8}$

$\underline{And}$

$\bold{y\:=\:6}$

$\bold{Sum\:of\:numbers\:=x\:+\:y}$

= $\bold{8\:+\:6\:=\:14}$

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