Question

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Answer 1

Step-by-step explanation:

let the smaller no. be x and bigger no. be y.

given, difference of the no. s is 4

y - x = 4 (x is smaller no. so it is written second).

then, sum of squares = 58

y^2 + x^2 = 58

y - x = 4

y = x+4 (substitute this value of y in y^2 + x^2=58)

(x + 4 )^2 + x^2 = 58

x^2 + 16 + 8x + x^2 = 58

2x^2 + 16 + 8x -58 = 0

2x^2 + 8x - 42 = 0

2x^2 + 14x -6x -42 = 0

2x( x + 7 ) - 6 ( x + 7) = 0

x + 7 = 0 ; 2x - 6 = 0 ;

x = -7 ; x = 3;

If x = -7 ,y = x + 4 ; y = -3

sum of smaller no.(x) and square of larger no. (y)

= -7 + (-3)^2

= -7 + 6

= -1

If x = 3; y = x + 4; y = 7;

sum of smaller no.(x) and square of larger no. (y)

= 3 + (7)^2

= 3 + 49

= 52.

Here the options are given for positive no.

hence,sum of smaller no.(x) and square of larger no. (y) = 52.

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