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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?
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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).
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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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If the sum and product of two numbers is 34 and 288 respectively, find the sum of their cubes.a)9236b)9928c)9854d)8352Correct answer is option 'B'. Can you explain this answer?
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