Question

Find the least value of 3x + 4y if x2y3 = 6.



a.13



b.10



c.14



d.15

Answer 1

Step-by-step explanation:

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Answer 2

The least value of 3x+4y is 10.

• Breaking the term 3x and 4y into 3x/2 , 3x/2 and 4y/3,4y/3,4y/3.

• Now we use Arithmetic and Geometric mean to find the least value of the expression.

AM >= GM     (Property of AM and GM)

AM of (3x/2,3x/2,4y/3,4y/3,4y/3) >= GM of (3x/2,3x/2,4y/3,4y/3,4y/3)

(3x/2+3x/2+4y/3+4y/3+4y/3)/5 >= (3/2×3/2×4/3×4/3×4/3)$^{1/5}$

(3x+4y)/5 >= ${(2^5)}^{1/5}$

(3x+4y) >= 2 × 5

(3x+4y) >= 10

• Minimum value of 3x+4y = 10