If b is the mean proportional of a and c then prove that a 2 + b 2 a b = a + c b

Given, b is the mean proportional of a and c . We have to prove that a 2 + b 2 a b = a + c b Two varying quantities are said to be in a relation of proportionality, multiplicatively connected to a constant; that is, when either their ratio or their product yields a constant. So, if a , b , c , d are in proportion, we can write it as a : b : : c : d , then a d = b c According to question, a : b : : b : c So, b 2 = a c ...... (1) Now, let us consider, L.H.S = a 2 + b 2 a b = a 2 + a c a b [Substituting (1)] = a ( a + c ) a b = a + c b = R.H.S Hence, a 2 + b 2 a b = a + c b proved.

E M B I B E

Mathematics Class - 10>Chapter 5 - Ratio and Proportion>Exercise – 2>Q 5

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10th Chhattisgarh Board

IMPORTANT

Earn 100

We have $100$ liters of a mixture of milk and water which is $10 %$ water. How much more pure milk should be added so that the new mixture has only $5 %$ water?

Important Questions on Ratio and Proportion

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10th Chhattisgarh Board

IMPORTANT

Mathematics Class - 10>Chapter 5 - Ratio and Proportion>Think and Discuss

Think of some examples of inverse proportions or inverse relations.

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10th Chhattisgarh Board

IMPORTANT

Mathematics Class - 10>Chapter 5 - Ratio and Proportion>Try this

Three persons $A, B and C$ can complete a task in $12, 15 and 10$ days respectively. If they all work together, how long will they take to complete the task?