THIRD FOURTH MEAN CONTINUED PROPORTION - PUNJAB-CURRICULUM-AND-TEXTBOOK-BOARD-PCTB / 10TH-CLASS / MATHEMATICS / MATHEMATICS-10-10TH-CLASS-NBF-2024 / VARIATIONS / THIRD-FOURTH-MEAN-CONTINUED-PROPORTION

We are already familiar with proportions that if quantities $a$ , $b$ , $c$ and $d$ are in proportion, then $a:b::c:d$

i.e., product of extremes $=$ product of means

If three quantities $a$ , $b$ and $c$ are related as $a:b::b:c$

then $c$ is called the third proportion.

Find a third proportional of $x + y$ and $x^2 - y^2$ .

Solution: Let $c$ be the third proportional,

x + y:x^2 -y^2::x^2 -y^2:c

c(x + y) = (x^2 -y^2)(x^2 -y^2)

3.1(ii) Find 3rd, 4th, mean and continued proportion