Question

A number is 7cm less than another number. If the sum of their squares is
169 find the numbers.​

Answer 1

Answer:

we can take the numbers= x,x+7

${x}^{2} + ({x + 7})^{2} = 169 \\ {x}^{2} + {x}^{2} + 14x + {7}^{2} = 169 \\ 2 {x}^{2} + 14x + 49 = 169 \\ 2 {x}^{2} + 14x = 169 - 49 = 120 \\ {x}^{2} + 7x = \frac{120}{2} = 60 \\ x(x + 7) = 8 60 \\ \frac{60}{x} = x + 7 \\ \\ x = 5 \\ x + 7 = 12$

Answer 2

Answer:

Let the number be x and the other number be y

According to 1st condition,

x - 7 = y

x - y = 7 -----(1)

According to 2nd condition,

x^2 + y^2 = 169

right

Squaring on both sides,we get

x + y = 13 -----(2)

Adding (1) & (2)

x - y = 7

+ x - y = 13

-----------------

2x = 20

x = 20

------

2

x = 10

Putting x = 10 in (2)

x + y = 13

20 + y = 13

y = 13 - 20

y = - 7

(x, y) = (10, - 7) is the solution of given equation

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