Positive numbers

Algebra Level 4

If $x$ and $y$ are positive numbers and $x^2+y^2=100$ , then which of the following value of $x$ gives the largest value of $x+y$ ?

6 10 7 9

1 solution

Nazmus Sakib
Mar 18, 2017

x = 7 We get 7² + y² = 100 Evaluate: 49 + y² = 100 Simplify: y² = 51 Solve: y = √51 NOTE: Recognize that √49 = 7 and √64 = 8. Since 51 is BETWEEN 49 and 64, √51 is BETWEEN 7 and 8. In other words, y = 7.something So x + y = 7 + 7.something = 14.something
x = 9 We get 9² + y² = 100 Evaluate: 81 + y² = 100 Simplify: y² = 19 Solve: y = √19 NOTE: We need not find the EXACT value of y here. We need only recognize that √16 = 4 and √25 = 5. Since 19 is BETWEEN 16 and 25, √19 is BETWEEN 4 and 5. In other words, y = 4.something So, x + y = 9 + 4.something = 13.something
x = 10 We get 10² + y² = 100 Evaluate: 100 + y² = 100 Simplify: y² = 0 Solve: y = 0 So x + y = 10 + 0 = 10
x = 6 We get 6² + y² = 100 Evaluate: 36 + y² = 100 Simplify: y² = 64 Solve: y = 8 So x + y = 6 + 8 = 14.

so ans is (7). because of that x+y get largest. :)