Question

Sum of squares of two positive numbers is 400. The difference of these two
numbers is 4. Determine the thrice of the bigger number.
48
36
42
30​

Answer 1

Answer:

1St Option

Explanation:

Given :-

Sum of squares of two positive numbers is 400. The difference of these two numbers is 4.

To find:-

Determine the thrice of the bigger number?

Solution:-

Let the two positive numbers be X and Y

Where X > Y

Given that

Sum of squares of two positive numbers =400.

X^2 + Y^2 = 400 ------------(1)

and

The difference of these two numbers = 4.

X - Y = 4

=> Y = X-4 --------------(2)

On Substituting this value in (1) then

=> X^2+(X-4)^2 = 400

=> X^2 + X^2 - 8X + 16 = 400

=> 2X^2 - 8X +16 = 400

=> 2X^2 - 8x + 16 -400 = 0

=> 2X^2 - 8X - 384 = 0

=> 2 (X^2 -4X - 192) = 0

=> X^2 - 4X - 192 = 0/2

=> X^2 - 4X - 192 = 0

=> X^2-16X +12X -192 = 0

=> X(X-16) +12(X-16) = 0

=> (X-16) (X+12) = 0

=> (X-16) = 0 or X+12 = 0

=> X=16 or X = -12

X cannot be negative.

X = 16

The bigger number = 16

Thrice of the number = 3X

=> 3(16)

= 48

Answer:-

Thrice of the bigger number for the given problem is 48

Check:-

X = 16

Y = 16-4 = 12

X^2 = 16^=256

Y^2=12^2 = 144

X^2+Y^2 = 256+144 = 400

Their difference = 16-12=4

Verified the given relations.

Answer 2

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Required number = 48

Given :-

• Sum of squares of two positive numbers is 400. The difference of these two numbers is 4.

To find:-

• Find the thrice of the bigger number?

Solution:-

• Let the two positive numbers be X and Y

• Where X > Y

Given that

• Sum of squares of two positive numbers =400.

• X^2 + Y^2 = 400 ------------(1)

and

• The difference of these two numbers = 4.

• X - Y = 4

• => Y = X-4 --------------(2)

On Substituting this value in (1) then

• => X^2+(X-4)^2 = 400

• => X^2 + X^2 - 8X + 16 = 400

• => 2X^2 - 8X +16 = 400

• => 2X^2 - 8x + 16 -400 = 0

• => 2X^2 - 8X - 384 = 0

• => 2 (X^2 -4X - 192) = 0

• => X^2 - 4X - 192 = 0/2

• => X^2 - 4X - 192 = 0

• => X^2-16X +12X -192 = 0

• => X(X-16) +12(X-16) = 0

• => (X-16) (X+12) = 0

• => (X-16) = 0 or X+12 = 0

• => X=16 or X = -12

X cannot be negative.

Therefore

• X = 16

The bigger number = 16

Thrice of the number = 3X

• => 3(16)

• = 48

Thus ,Thrice of the bigger number for the given problem is 48

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