Question

The number X is 2 more than number y. if the sum of the squares of X and Y is 34 find the product of X and y. I have given answer

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Answer 1

Answer:

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Let the first number x and the ither number be y .

Therefore ,

According to the conditions ;

x = y + 2 ----(1)

x^2 + y^2 = 34 -----(2)

substituting eq (1) in eq(2)

(y +2)^2 + y^2 = 34

y^2 + 4y +4 + y^2 = 34

2y^2 + 4y + 4 = 34

y^2 + 2y + 2 = 17

y^2 + 2y -15 = 0

y^2 - 3y + 5y - 15 =0

y (y-3) + 5( y - 3 ) =0

(y - 3 )( y + 5 ) = 0

Therefore

y = 3 and y = -5

Case 1

y = 3

subsituting y = 3 in eq (1)

x = 3 +2

x = 5

Case 2

y = -5

substituting y =-5 in eq (1)

x = -5 +2

x = -3

Therefore ;

x = 5 and y = 3 and

x = -3 and y = -5

Therefore ;

Case 1

xy = 5 × 3

= 15

Case 2

xy = -3 × -5

= 15

Hence proved