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The sum of squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, then what is the difference of the larger and smaller numbers.
- a)2
- b)3
- c)4
- d)6
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The sum of squares of two positive integers is 208. If the square of t...
Suppose the numbers are ‘a’ and ‘b’ with a > b
a2 + b2 = 208 and a2 = 18b
Solving the equations
⇒ b2 + 18b = 208
⇒ b2 + 18b – 208 = 0
⇒ (b + 26)(b – 8) = 0
⇒ b = 8, b = -26
If b = 8
a2 = 18b = 18 × 8 = 144
⇒ a = 12
∴ Difference of the larger and the smaller number = 12 – 8 = 4
a2 + b2 = 208 and a2 = 18b
Solving the equations
⇒ b2 + 18b = 208
⇒ b2 + 18b – 208 = 0
⇒ (b + 26)(b – 8) = 0
⇒ b = 8, b = -26
If b = 8
a2 = 18b = 18 × 8 = 144
⇒ a = 12
∴ Difference of the larger and the smaller number = 12 – 8 = 4
Most Upvoted Answer
The sum of squares of two positive integers is 208. If the square of t...
Given information:
Sum of squares of two positive integers = 208
Square of the larger number = 18 times the smaller number
Let's assume the smaller number as x and the larger number as y.
Sum of squares equation:
x^2 + y^2 = 208
Square equation:
y^2 = 18x
We need to find the difference between the larger and smaller numbers, which is y - x.
To solve this problem, we can use substitution or elimination method.
Using Substitution Method:
Substitute the value of y^2 from the second equation into the first equation:
x^2 + 18x = 208
Rearrange the equation:
x^2 + 18x - 208 = 0
Factorize the equation:
(x - 8)(x + 26) = 0
From this, we get two possible values for x: x = 8 or x = -26.
Since we are looking for positive integers, we discard the negative value.
Now, substitute the value of x back into the second equation to find y:
y^2 = 18 * 8
y^2 = 144
y = 12
So, the smaller number is 8 and the larger number is 12.
The difference between the larger and smaller numbers is 12 - 8 = 4.
Therefore, the correct answer is option C) 4.
Sum of squares of two positive integers = 208
Square of the larger number = 18 times the smaller number
Let's assume the smaller number as x and the larger number as y.
Sum of squares equation:
x^2 + y^2 = 208
Square equation:
y^2 = 18x
We need to find the difference between the larger and smaller numbers, which is y - x.
To solve this problem, we can use substitution or elimination method.
Using Substitution Method:
Substitute the value of y^2 from the second equation into the first equation:
x^2 + 18x = 208
Rearrange the equation:
x^2 + 18x - 208 = 0
Factorize the equation:
(x - 8)(x + 26) = 0
From this, we get two possible values for x: x = 8 or x = -26.
Since we are looking for positive integers, we discard the negative value.
Now, substitute the value of x back into the second equation to find y:
y^2 = 18 * 8
y^2 = 144
y = 12
So, the smaller number is 8 and the larger number is 12.
The difference between the larger and smaller numbers is 12 - 8 = 4.
Therefore, the correct answer is option C) 4.
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The sum of squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, then what is the difference of the larger and smaller numbers.a)2b)3c)4d)6Correct answer is option 'C'. Can you explain this answer?
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