perplexus.info :: Just Math : Given Linear Sum, Find the Sum of Exponents

Given Linear Sum, Find the Sum of Exponents (Posted on 2024-05-19)

Each of x and y is a real number that satisfies this equation:
2x + y = -6

Determine the minimum value of this expression:

(1/4)^x + (1/2)^y

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

by graphing

| Comment 2 of 3 |

Since y = -6 - 2*x, plot a function where that substitution is made for y:

fplot(@(x)(1/4)^x+(1/2)^(-6-2*x),[-3 .5])

grid

shows the minimum sum is 16, at x = -1.5, y = -3.

Posted by Charlie on 2024-05-19 08:53:34

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