If a- b-and c are in A-P- p- q- and r are in H-P- and a p- b q- and c r are in G-P- then p-r-r-p is equal to

The correct option is B p/r+r/p=p^2+r^2/pr=(p+r)^2 2pr/pr =4p^2r^2/q^2 2pr/pr =4pr/q^2 2=4b^2/ac 2 [∵ ap,bq,cr are in A.P.⇒ b^2q^2=acpr] =(a+c)^2/ac 2 [a,b,c ...

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Byju's Answer

Standard XI

Mathematics

Sum of product of binomial coefficients

If a, b,and c...

Question

If a, b,and c are in A.P., p, q, and r are in H.P. and ap, bq, and cr are in G.P., then $\frac{p}{r} + \frac{r}{p}$ is equal to

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Solution

The correct option is B

$\frac{p}{r} + \frac{r}{p} = \frac{p^{2} + r^{2}}{p r} = \frac{(p + r)^{2} - 2 p r}{p r}$

$= \frac{\frac{4 p^{2} r^{2}}{q^{2}} - 2 p r}{p r}$

$= \frac{4 p r}{q^{2}} - 2 = \frac{4 b^{2}}{a c} - 2$

$[∵ a p, b q, c r a r e i n A . P . \Rightarrow b^{2} q^{2} = a c p r]$

$= \frac{(a + c)^{2}}{a c} - 2 [a, b, c a r e i n A . P \Rightarrow .2 b = a + c]$

$\frac{a}{c} + \frac{c}{a}$

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If a, b,and c are in A.P., p, q, and r are in H.P. and ap, bq, and cr are in G.P., then pr+rp is equal to

The correct option is B pr+rp=p2+r2pr=(p+r)2−2prpr =4p2r2q2−2prpr =4prq2−2=4b2ac−2 [∵ap,bq,cr are in A.P.⇒b2q2=acpr] =(a+c)2ac−2[a,b,c are in A.P⇒.2b=a+c] ac+ca

If a, b,and c are in A.P., p, q, and r are in H.P. and ap, bq, and cr are in G.P., then $\frac{p}{r} + \frac{r}{p}$ is equal to