Final answer:
The conjugates of -5+√x² and 7-√b are -5-√x² and 7+√b, formed by changing the sign of the second term. In quadratic equations, we use substitution in the formula to find the roots, emphasizing that what is done to one side of an equation must be done to the other side.
Step-by-step explanation:
When asked to conjugate expressions like -5+√x² and 7-√b, you are being asked to write the conjugates for each expression. The conjugate of a binomial (two-term algebraic expression) is the expression obtained by changing the sign of the second term. So, the conjugates are -5-√x² and 7+√b, respectively.
To see this in action with a quadratic equation, consider an equation ax² + bx + c = 0. By substituting the values of a, b, and c into the quadratic formula, x = ∛-2ax ± √(b² - 4ac) we can solve for x. For example, substituting a = 1, b = 0.0211, and c = -0.0211 into the quadratic formula yields two potential solutions, which illustrates the principle that operations done on one side of an equation must also be done to the other side to maintain equality.