Question

If a, b are positive real numbers such that the lines ax + 9y = 5 and 4x + by = 3 are parallel, then the least possible value of a + b is

Answer 1

Answer:

slope of ax + 9y = 5 = -a/9 =m1

slope of 4x+by = 3 = -4/b =m2

since lines are parallel,

m1 = m2

-a/9 = -4/b

ab = 36

Now, using AM≥GM ,

(a+b) ≥ 2√ab

(a+b)≥ 2*√36

(a+b) ≥ 12

so, least possible value = 12 (Ans)

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Answer 2

Answer:

The least possible value of a + b is 12

Explanation:

Two lines are parallel if and only if their slopes are equal.

a/4 = 9/b

ab =36

a+b would be minimum when a and b are equal

The least possible value of a + b is 12

Real number :

The real number is a number that can be used to represent a continuous one-dimensional quantity in mathematics, such as a temperature, time, or distance. Continuous in this context implies that values may vary by arbitrary little amounts. In the real number system, a number that is less than zero is considered a negative number. Sometimes a loss or deficit is expressed as a negative number. Real numbers include the number zero and can be either positive or negative.

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