MathematicsIf a3+b3=75 , where a,b∈N , then the number of possible ordered pairs of the form (a,b) can be obtained is

If $a \sqrt{3} + b \sqrt{3} = \sqrt{75}$ , where $a, b \in N$ , then the number of possible ordered pairs of the form $(a, b)$ can be obtained is

a \sqrt{3} + b \sqrt{3} = \sqrt{75}

$a \sqrt{3} + b \sqrt{3} = 5 \sqrt{3}$

$(a + b) \sqrt{3} = 5 \sqrt{3}$

$a + b = 5$

Possible ordered pairs ${(1, 4), (2, 3), (3, 2), (4, 1)}$

No., of possible ordered pairs is 4.

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