Question

find fourth proportional to:
a³-b³,a⁴+a²b²+b⁴,a-b

no wrong answers or
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​

Answer 1

Step-by-step explanation:

Let the fourth proportional be x.

$( {a}^{3} - {b}^{3}) : ( {a}^{4} + {a}^{2} {b}^{2} + {b}^{4}) = \\ ( {a} - {b}) : x$

$x = \frac{( {a}^{4} + {a}^{2} {b}^{2} + {b}^{2}) \times (a \: - b)}{ {a}^{3} - {b}^{3} }$

$x = \frac{( {a}^{4} + {a}^{2} {b}^{2} + {b}^{2}) \times (a \: - b)}{ ({a} - {b})( {a}^{2} + ab \: + {b}^{2} )}$

$x = \frac{( {a}^{4} + {a}^{2} {b}^{2} + {b}^{4}) }{( {a}^{2} + ab \: + {b}^{2} )}$

$x = \frac{( {a}^{2} + {a} {b} + {b}^{2})( {a}^{2} \: - ab + {b}^{2}) }{( {a}^{2} + ab \: + {b}^{2} )}$

$x = {a}^{2} - ab + {b}^{2}$

Hence, the answer.