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RonL
Hello, jaswinder!
The combined heights of two cubes are 11 m
and their combined volumes equal 407 m³.
Calculate the dimentions of each cube.
Let the heights of the cubes be x and y.
We have: . x + y .= .11 . → . y .= .11 - x .[1]
. . . and: .x³ + y³ .= .407 .[2]
Substitute [1] into [2]: .x³ + (11 - x)³ .= .407
. . . . . . x³ + 1331 - 363x + 33x² - x³ .= .407
. . . . . . . . . . . . . .33x² - 363x + 924 .= .0
Divide by 33: . x² - 11x + 28 .= .0
. . . . Factor: . .(x - 4)(x - 7) .= .0
And we have: .x .= .4, 7 . → . y .= .7, 4
Therefore, the heights of the cubes are 4 m and 7 m.