Question
Download Solution PDFIf the sum of squares of two real numbers is 26 and their sum is 6 then the sum of cubes of these two numbers is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Let the two real numbers be x and y.
Sum of squares: x2 + y2 = 26
Sum of the numbers: x + y = 6
Formula Used:
(x + y)2 = x2 + y2 + 2xy
x3 + y3 = (x + y)(x2 + y2 - xy)
Calculations:
x + y = 6
(x + y)2 = 62
x2 + y2 + 2xy = 36
26 + 2xy = 36
2xy = 36 - 26
2xy = 10
xy = 5
Now, we need to find the sum of the cubes, x3 + y3:
x3 + y3 = (x + y)(x2 + y2 - xy)
Substitute the known values of x + y, x2 + y2, and xy:
x3 + y3 = (6)(26 - 5)
x3 + y3 = (6)(21)
x3 + y3 = 126
∴ The sum of the cubes of the two numbers is 126.
Last updated on Feb 17, 2025
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