Subject: Mathematics
Topic: Applying the Fundemental Theorems of Proportionality to Solve Problems Involving Proportions
Problem/Question: Solve for the u:v if u[tex]^{2}[/tex] + 3uv – 10v[tex]^{2}[/tex] = 0
Topic: Applying the Fundemental Theorems of Proportionality to Solve Problems Involving Proportions
Problem/Question: Solve for the u:v if u[tex]^{2}[/tex] + 3uv – 10v[tex]^{2}[/tex] = 0
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Answer:
-5 or 2
Step-by-step explanation:
u² + 3uv - 10v² = 0
u² - 2uv + 5uv - 10v² = 0
u(u - 2v) + 5v(u - 2v) = 0
(u + 5v)(u - 2v) = 0
Two different factors has a product of zero, so by zero-product property, either one of the factors is equal to zero (or both), i.e.
u + 5v = 0 or u - 2v = 0
u = -5v or u = 2v
This gives us u:v = -5 or u:v = 2