If p:q is the sub duplicate ratio of p-x square : q-x square then x Square is?

Question

Answer

Explanation:

Given p:q is the sub duplicate ratio of p-x square : q-x square, we need to find x square.

Step 1: Understanding Sub Duplicate Ratio

Sub Duplicate Ratio is a ratio of two numbers such that the ratio of the larger number to their difference is equal to the ratio of their difference to the smaller number.

In other words, if a:b is the sub duplicate ratio of c:d, then:

a/b = (c+d)/c and b/a = c/(c+d)

Step 2: Applying Sub Duplicate Ratio

Let p:q be the sub duplicate ratio of p-x square : q-x square.

Then, we can write:

p/q = [(p-x square) + (q-x square)]/(p-x square)

Using the formula for a+b whole square, we can simplify this expression as:

p/q = [(p+q) - 2x square]/(p-x square)

or, p/q = (p+q)/(p-x square) - 2x square/(p-x square)

or, p/q = (p+q)/(p-x square) - 2x square/p-q

Now, we can cross-multiply to get:

p(p-q) = q(p+q) - 2x square p-q

or, p square - pq = pq + q square - 2x square p + 2x square q

or, 2x square p - 2x square q = p square + q square - pq - pq

or, x square = (p square + q square - pq)/(2p - 2q)

Step 3: Simplifying x Square

We can further simplify x square as:

x square = [(p+q)^2 - 3pq]/[2(p-q)]

Step 4: Final Answer

Therefore, the value of x square is [(p+q)^2 - 3pq]/[2(p-q)].

Answer

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