Determine the Value of x+2y

Determine the Value of x+2y

Solution:

Given the two equations: ……(i), and …..(ii), to determine the Value of x+2y, the following steps are necessary:

Step 1: Consider equation (i) above , x²+4y²=40. Supposing that (x+2y)²=p……(iii) is an equation that will produce x²+4y² among its constituents when expanded, expanding (x+2y)²=p produces;

Step 2: Regrouping equation (iv) above results in the following equation:

4(xy) +(x²+4y²)=p………(v)

Step 3: Given that x²+4y² and xy equal to 40 and 6, respectively, substituting their quantities into equation (v) above gives:

p=(40)+4(6)

p=40+24

p=64

Step 4: Substituting for the Value of p in equation (iii) above yields:

64=(x+2y)²

Step 5: To determine the Value of x+2y, first, calculate the square root of either side of the equation. Note that there are two possible roots, a positive and a negative.

Verification: