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.
| x+2y=8 or -8 |
Verification: