If b is the mean proportional between a and c , prove that a, c, a 2 + b 2 and b 2 + c 2 are proportional.

Given, b is the mean proportional between a and c then, b 2 = ac. [....Eq 1] If a, c, a 2 + b 2 and b 2 + c 2 are proportional then, Solving L.H.S first a(b 2 + c 2 ) = a(ac + c 2 ) [Putting value of b 2 from Eq 1] = ac(a + c) Solving R.H.S c(a 2 + b 2 ) = c(a 2 + ac) [Putting value of b 2 from Eq 1] = ac(a + c) Since, L.H.S. = R.H.S = ac(a + c), hence the numbers, a, c, a 2 + b 2 and b 2 + c 2 are in proportion.

What numbers must be added to each of the numbers 16, 26 and 40 so that the resulting numbers must be in continued proportion?

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Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.

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If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).

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If y is the mean proportional between x and z, prove that
xyz(x + y + z)³ = (xy + yz + zx)³

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Mathematics

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

Ratio Proportion

Related Questions

What numbers must be added to each of the numbers 16, 26 and 40 so that the resulting numbers must be in continued proportion?

Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.

If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).

If y is the mean proportional between x and z, prove that
xyz(x + y + z)³ = (xy + yz + zx)³

Mathematics

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

Ratio Proportion

Related Questions

What numbers must be added to each of the numbers 16, 26 and 40 so that the resulting numbers must be in continued proportion?

Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.

If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a2 + b2) and (b2 + c2).

If y is the mean proportional between x and z, prove thatxyz(x + y + z)3 = (xy + yz + zx)3

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

If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).

If y is the mean proportional between x and z, prove that
xyz(x + y + z)³ = (xy + yz + zx)³