$x^{2} (\frac{1}{10})^{2} + (1 - x)^{2} (\frac{4}{10})^{2} = (\frac{2}{10})^{2}$

Answer

The equation has an infinite number of solutions.

Explanation

x^{2} (\frac{1}{10})^{2} + (1 - x)^{2} (\frac{4}{10})^{2} 10 x^{2} (\frac{1}{10})^{2} + 10 (1 - x)^{2} (\frac{4}{10})^{2} 0 + 10 (1 - x)^{2} \cdot 0.16 0 + 10 (1 - 2 x + x^{2}) \cdot 0.16 0 + (10 - 20 x + 10 x^{2}) \cdot 0.16 0 + 0 + 0 x + 0 x^{2} 0 = (\frac{2}{10})^{2} = 10 (\frac{2}{10})^{2} = 0 = 0 = 0 = 0 = 0 multiply ALL terms by 10 . cancel out the denominators simplify left side

Since the statement $0 = 0$ is TRUE for any value of $x$ , we conclude that the equation has infinitely many solutions.

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x2(101​)2+(1−x)2(104​)2=(102​)2

The equation has an infinite number of solutions.

$x^{2} (\frac{1}{10})^{2} + (1 - x)^{2} (\frac{4}{10})^{2} = (\frac{2}{10})^{2}$