The length of the rectangular field is cube root of 5 + cube root of 2. Find the measure of it's breadth such that area of the rectangle is rational number.
Answers
breadth of rectangle = {5⅔ + 2⅔ - 10⅓}
length of a rectangular field is ³√5 + ³√2
we have to find breadth such that the area of the rectangle is a rational number.
as we know, area of rectangle = length × breadth
let's apply this application here.
as length of rectangle = ³√5 + ³√2
let a = ³√5 , b = ³√2
a³ = 5 and b³ = 2
so, a³ + b³ = (a + b)(a² + b² - ab)
⇒5 + 2 = (³√5 + ³√2){(³√5)² + (³√2)² - (³√5)(³√2)}
⇒7 = (³√5 + ³√2){5⅔ + 2⅔ - 10⅓} this expression seems like area of rectangle = length × breath
so, breadth of rectangle = {5⅔ + 2⅔ - 10⅓}
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