Question

Найдите область определения выражения (х-3)(5-х) всё под корнем

Answer 1

(х-3)(5-х)
х+х=5+3
2х=8
х=8:2
х=4

Answer 2

Finding the Domain of the Expression (x-3)(5-x) under the Square Root

To find the domain of the expression \((x-3)(5-x)\) under the square root, we need to determine the values of \(x\) for which the expression under the square root is non-negative.

The expression \((x-3)(5-x)\) simplifies to \(x^2 - 2x - 15\). To find the domain, we need to ensure that the expression \(x^2 - 2x - 15\) is non-negative.

Determining the Domain

The domain of the expression \((x-3)(5-x)\) under the square root is the set of all real numbers \(x\) for which \(x^2 - 2x - 15 \geq 0\).

Solution

The domain of the expression \((x-3)(5-x)\) under the square root is the set of all real numbers \(x\) such that \(x^2 - 2x - 15 \geq 0\).

Citing the Relevant Search Snippet

The expression \((x-3)(5-x)\) simplifies to \(x^2 - 2x - 15\), and we need to find the values of \(x\) for which the expression under the square root is non-negative.

Therefore, the domain of the expression \((x-3)(5-x)\) under the square root is the set of all real numbers \(x\) for which \(x^2 - 2x - 15 \geq 0\.

I hope this helps! If you have further questions, feel free to ask.