Directions: Solve the following problems.
1. Find two numbers such that the square root of their sum is 5 and the square root of their product is 12.
2. If 4 is added to the square root of a number, the result is 1. Is there a real number solution? If yes, what is
the number? If none explain why?​


Sagot :

Answer:

1. No real number solution.

We can attempt to solve as a system of two equations; Let x and y be the two numbers.

Equation 1) xy = 12

Equation 2) x + y = 5

In Equation 2) y = 5 - x;

In Equation 1) x(5 - x) = 12; 5x - x^2 - 12;then x^2 - 5x +12 = 0

There are no integral factors or numeric factors of 12 that have a sum of -5 in the quadratic equation to establish two binomial factors of the quadratic.

Using a TI-81 Graphing Calculator, shows Graph of Equation 1) a hyperbola in quadrants ONE and THREE. The Graph of Equation 2) is a linear line having a slope of -1 and y-intercept of 5, the line never intersects the hyperbola in quadrant ONE or any other quadrant. This suggests no real number solution for the described number relationships.

2. No  ,because there has no real numbers

Step-by-step explanation: