Question

26. The third proportional to x - y and x²- y² is :​

Answer 1

Step-by-step explanation:

Given :-

x-y and x²-y²

To find :-

Third Proportional

Solution :-

Given that

(x-y) and (x²-y²)

Let the third proportional of (x-y) and (x²-y²) be A

then , (x-y) : (x²-y²) : : (x²-y²) : A

Product of means = (x²-y²)×(x²-y²)

Product of extremes = (x-y)×A

We know that

In Proportion , Product of means = Product of extremes

=> (x²-y²)×(x²-y²) = (x-y)×A

=> (x+y)(x-y)(x²-y²) = (x-y)×A

On cancelling (x-y) both sides then

=> (x+y)(x²-y²) = A

Therefore, A = (x+y)(x²-y²) or

=> A = x(x²-y²)+y(x²-y²)

=> A = x³-xy²+x²y-y³

Therefore, A = x³-xy²+x²y-y³

Answer:-

The third proportional is (x+y)(x²-y²) or x³-xy²+x²y-y³

Used formulae:-

→ If a, b and c are in continued proportion ( a : b : : b : c ) then c is called third proportional of a and b.

→ In proportion, Product of means = Product of extremes

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Given :-

x-y and x²-y²

To find :-

Third Proportional

Solution :-

Given that

(x-y) and (x²-y²)

Let the third proportional of (x-y) and (x²-y²) be A

then , (x-y) : (x²-y²) : : (x²-y²) : A

Product of means = (x²-y²)×(x²-y²)

Product of extremes = (x-y)×A

We know that

In Proportion , Product of means = Product of extremes

=> (x²-y²)×(x²-y²) = (x-y)×A

=> (x+y)(x-y)(x²-y²) = (x-y)×A

On cancelling (x-y) both sides then

=> (x+y)(x²-y²) = A

Therefore, A = (x+y)(x²-y²) or

=> A = x(x²-y²)+y(x²-y²)

=> A = x³-xy²+x²y-y³

Therefore, A = x³-xy²+x²y-y³

Answer:-

The third proportional is (x+y)(x²-y²) or x³-xy²+x²y-y³

Used formulae:-

→ If a, b and c are in continued proportion ( a : b : : b : c ) then c is called third proportional of a and b.

→ In proportion, Product of means = Product of extremes

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