Question

the difference of two number is 2 and sum of their sqaure is 34.find the numbers. ​

Answer 1

let the numbers be x and y ( y>x )

so y-2 = x

y = x+2 ............. 1

sum of their squares =>

x²+ (x+2)² =34

=> x²+x²+4+4x = 34

=> 2x²+4x = 30

=> x²+2x-15 = 0

=> by quadratic formula =>

-2+-√4+60/2

=> for +

-2+8/2 => 3

for -

-2-8/2 => -5

so the numbers can be 3 and 5

and -3 and -5

Answer 2

The number can be -5 and -3 or 5 and 3

Step-by-step explanation:

Let the two numbers be x and y

We are given that the difference of two number is 2

So, x-y=2

So, x = 2+y -- A

We are also given that sum of their sqaure is 34.

$x^2+y^2=34$

using A

$(2+y)^2+y^2=34\\4+y^2+4y+y^2=34\\2y^2+4y+4=34\\y^2+2y+2=17\\y^2+2y-15=0\\y^2+5y-3y-15=0\\(y+5)(y-3)=0\\y=-5,3$

When y =-5

x=2+y=2-5=-3

When y = 3

x=2+y=2+3=5

So, the number can be -5 and -3 or 5 and 3

#Learn more:

the difference of two number is 2 and sum of their sqaure is 34.find the numbers. ​

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