Question

Two positive numbers differ by 7 and the sum of their squares is 169. Find the numbers​

Answer 1

Answer:

$\large\bf\underline{question}$

Two positive numbers differ by 7 and the sum of their squares is 169. Find the numbers

$\large\bf\underline{given}$

•difference of two positive number = 7

•square of the two positive number = 169

$\large\bf\underline{to\:find}$

two positive numbers

$\large\bf\underline{solution}$

Let x be the larger of the 2 positive numbers

Let y be the smaller of the 2 positive numbers

${x}^{2} + {y}^{2} = 169$

$x - y = 7$

$➔ \: x = 7 + y$

⠀

${x}^{2} + {y}^{2} = 169$

$➔ {(y + 7)}^{2} + {y}^{2} = 169$

$➔ {y}^{2} + 14y + 49 + {y}^{2} = 169$

$➔ {2y}^{2} + 14y - 120 = 0$

$➔2( {y}^{2} + 7y - 60) = 0$

$➔ {y}^{2} + 7y - 60 = 0$

$➔(y + 12)(y - 5) = 0$

$➔y = \: - 12 \: \: \: \: \: \: \: \: \: \: \: \: y = 5$

$however \: we \: want \: y > 0$

➔$\tt\underline\red{y = 5}$

$x - y = 7$

$➔x - 5 = 7$

➔$\tt\underline\red{x\:=\:12}$

Answer 2

Answer:

x = 5 y= 7

Step-by-step explanation:

the answer is attached above

steps: first we take the above 2 equations and simplify them to solve a quadratic equation

then we use quadratic equation to solve the equation

we get 2 values one positive and 1 negetive

we take the positive integer because it is mentioned positive integers in the question