If √8-a + √5+a = 5, then √(8-a)(5+a) = ...
Please help me solve this.
Let's see if we can get to √(8-a)(5+a) from the following equation:
√(8-a) + √(5+a) = 5
Start by squaring both sides (whatever operation you do to one side of an equation you must do to the other side as well):
[√(8-a) + √(5+a)]^2 = 5^2
8 - a + 2√(8-a)(5+a) + 5 + a = 25
2√(8-a)(5+a) = 12
Divide both sides by 2:
√(8-a)(5+a) = 6 --->your answer
I hope this will help.
Helped alot! Thank you!
To solve this problem, we can follow these steps:
1. Start by simplifying the equation √8 - a + √5 + a = 5.
Notice that the terms with 'a' have opposite signs, which means they cancel each other out. Therefore, we can simplify the equation to √8 + √5 = 5.
2. To find the value of √(8 - a)(5 + a), we need to first simplify the expression inside the square root.
Expand the expression (8 - a)(5 + a) using the distributive property:
(8 - a)(5 + a) = 8(5) + 8(a) - a(5) - a(a)
= 40 + 8a - 5a - a^2
3. Simplify the expression (8 - a)(5 + a) by combining like terms.
(8 - a)(5 + a) = 40 + 3a - a^2
4. Substitute the value of √8 + √5 from step 1 into the simplified expression.
√(8 - a)(5 + a) = √(40 + 3a - a^2)
5. Therefore, the expression √(8 - a)(5 + a) is equal to √(40 + 3a - a^2).
Note: It is important to remember that we cannot simplify the expression any further without knowing the value of 'a'.