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If the sum and product of two numbers is 34 and 288 respectively, find the sum of their cubes.
- a)9236
- b)9928
- c)9854
- d)8352
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the sum and product of two numbers is 34 and 288 respectively, find...
Let's assume the two numbers as x and y.
We are given that the sum of the two numbers is 34, so we can write the equation as:
x + y = 34 ...(1)
We are also given that the product of the two numbers is 288, so we can write the equation as:
xy = 288 ...(2)
To find the sum of their cubes, we need to find the values of x and y first.
Solving the equations:
From equation (1), we can express y in terms of x:
y = 34 - x
Substituting this value of y in equation (2), we get:
x(34 - x) = 288
Expanding the equation:
34x - x^2 = 288
Rearranging the equation:
x^2 - 34x + 288 = 0
Now we can solve this quadratic equation to find the values of x.
Factoring the equation:
(x - 16)(x - 18) = 0
Setting each factor equal to zero:
x - 16 = 0 or x - 18 = 0
Solving for x, we have two possible solutions:
x = 16 or x = 18
Now we can find the corresponding values of y:
For x = 16, y = 34 - 16 = 18
For x = 18, y = 34 - 18 = 16
So the two numbers are 16 and 18.
Finding the sum of their cubes:
16^3 + 18^3 = 4096 + 5832 = 9928
Hence, the sum of their cubes is 9928, which corresponds to option (b).
We are given that the sum of the two numbers is 34, so we can write the equation as:
x + y = 34 ...(1)
We are also given that the product of the two numbers is 288, so we can write the equation as:
xy = 288 ...(2)
To find the sum of their cubes, we need to find the values of x and y first.
Solving the equations:
From equation (1), we can express y in terms of x:
y = 34 - x
Substituting this value of y in equation (2), we get:
x(34 - x) = 288
Expanding the equation:
34x - x^2 = 288
Rearranging the equation:
x^2 - 34x + 288 = 0
Now we can solve this quadratic equation to find the values of x.
Factoring the equation:
(x - 16)(x - 18) = 0
Setting each factor equal to zero:
x - 16 = 0 or x - 18 = 0
Solving for x, we have two possible solutions:
x = 16 or x = 18
Now we can find the corresponding values of y:
For x = 16, y = 34 - 16 = 18
For x = 18, y = 34 - 18 = 16
So the two numbers are 16 and 18.
Finding the sum of their cubes:
16^3 + 18^3 = 4096 + 5832 = 9928
Hence, the sum of their cubes is 9928, which corresponds to option (b).
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Community Answer
If the sum and product of two numbers is 34 and 288 respectively, find...
Let the numbers be ‘x’ and ‘y’
Given, sum = x + y = 34
Product = xy = 288
As we know, x3 + y3 = (x + y)3 – 3xy(x + y) = (x + y)[(x + y)2 – 3xy]
∴ Sum of their cubes = 34 × [(34)2 – 3 × 288] = 34 × (1156 – 864) = 34 × 292 = 9928
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