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How to apply Componendo and dividendo in this: E1+E2E1−E2=51

How to apply Componendo and dividendo in this:
E1+E2E1−E2=51

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Hint: Assume a=E1+E2,b=E1−E2,c=5,d=1 from the equation and apply componendo and dividendo theorems to solve for E1,E2 . Formulas used: If a, b, c, d are numbers and ab=cd , then Componendo is a+bb=c+dd Dividendo is a−bb=c−dd Complete step-by-step answer: We are given E1+E2E1−E2=51 and we have to apply the componendo and dividendo a=E1+E2,b=E1−E2,c=5,d=1 Componendo: a+bb=c+dd→(E1+E2)+(E1−E2)(E1−E2)=5+11→E1+E1+E2−E2E1−E2=61→2E1E1−E2=61→2E1=6(E1−E2)→2E1=6E1−6E2→6E2=6E1−2E1→6E2=4E1→E1E2=64=32 Dividendo: a−bb=c−dd→(E1+E2)−(E1−E2)(E1−E2)=5−11→E1−E1+E2+E2E1−E2=41→2E2E1−E2=41→2E2=4(E1−E2)→2E2=4E1−4E2→2E2+4E2=4E1→6E2=4E1→E1E2=64=32 Therefore, applied componendo and dividendo to get the ratio of E1,E2 Note: A theorem on proportions which is used to perform calculations and reduce the number of steps can be termed as componendo and dividendo. Some of its applications include the solving of equations involving fractions or rational functions, in mathematical Olympiads. According to componendo and dividendo, if a/b = c/d, then (a+b) / (a-b) = (c+d) / (c-d). Here are the rules based on componendo and dividendo- If a, b, c and d are numbers and b, d are non zero and a/b = c/d then, the following holds: 1. Componendo (a+b)/b = (c+d)/d. 2. Dividendo: (a-b)/b = (c-d)/d 3. For k not equal to (a/b), (a+kb)/(a-kb)=. (c+kd)/(c-kd). 4. And also for k not equal to (-b/d), (a/b) = (a+kc)/(b+kd). Don’t confuse componendo with dividendo. As in componendo we add the denominator to numerator and in dividendo we subtract denominator from numerator.

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