If b is the mean proportional between a and c, prove that a, c, a2 + b2 and b2 + c2 are proportional.

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deepaksoniGuru

Asked: March 18, 20212021-03-18T12:01:35+05:30 2021-03-18T12:01:35+05:30In: ICSE

This is an important ques from the Book ML Aggarwal class 10th,, chapter – 7, ratio and proportion.

It is given that b is the mean proportional between a and c, and we have to prove that a, c, a² + b² and b² + c² are proportional.

Question 12, exercise 7.2

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AAREKH · Answer 1 · 2021-03-20T11:50:33+05:30

AAREKH Guru

Solution:

It is given that

b is the mean proportional between a and c

We can write it as

b² = a × c

b² = ac ….. (1)

We know that

a, c, a² + b² and b² + c² are in proportion

It can be written as

a/c = (a² + b²)/ (b² + c²)

By cross multiplication

a (b² + c²) = c (a² + b²)

Using equation (1)

a (ac + c²) = c (a² + ac)

So we get

ac (a + c) = a²c + ac²

Here ac (a + c) = ac (a + c) which is true.

Therefore, it is proved.