Home
Class 12
MATHS
Suppose a,b,c are in AP and a^(2),b^(2),...

Suppose `a,b,c` are in AP and `a^(2),b^(2),c^(2)` are in GP, If `agtbgtc` and `a+b+c=(3)/(2)`, than find the values of a and c.

Text Solution

Verified by Experts

Since, a,b,c are in AP and sum of a,b,c is given.
Let `a=b-D,c=b+D " " [Dlt0][therefore agtbgtc]`
and given `a+b+c=(3)/(2)`
`implies b-D+b+b+D=(3)/(2)`
` therefore b=(1)/(2)`
Then, `a=(1)/(2)-D` and `c=(1)/(2)+D`
Also, given `a^(2),b^(2),c^(2)` are in GP, than `(b^(2))^(2)=a^(2)c^(2)`
`implies pm b^(2)=ac implies pm (1)/(4)=(1)/(4)-D^(2)`
`impliesD^(2)=(1)/(4) pm (1)/(4)=(1)/(2) " "[therefore D ne 0]`
`therefore D=pm (1)/(sqrt2) implies D=-(1)/(sqrt2)" "[therefore Dlt0]`
Hence, `a= (1)/(2)+(1)/(sqrt2) " and " c=(1)/(2)-(1)/(sqrt2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If a,b,c are in AP and a^(2),b^(2),c^(2) are in HP, then

If a,b,c are three terms in A.P and a^(2), b^(2), c^(2) are in G.P. and a + b + c = (3)/(2) then find a. (where a lt b lt c )

If the points A(-1, -4) , B(b,c) and C(5,-1) are collinear and 2b + c = 4 , find the values of b and c.

If a, b and c are in GP, then the value of (a-b)/(b-c) is equal to……..

a,b,c,d are in G.P. Prove that a^(2)-b^(2),b^(2)-c^(2), c^(2)-d^(2) are also in G.P.

If a,b,c are in AP and (a+2b-c)(2b+c-a)(c+a-b)=lambdaabc , then lambda is

If a , b , c , are in A P ,a^2,b^2,c^2 are in HP, then prove that either a=b=c or a , b ,-c/2 from a GP (2003, 4M)

If x^2+3x+5=0 and a x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+c .

If a + b +c =9 and ab + bc + ca =26, then find a ^(2) + b ^(2) + c ^(2).

If a+b+c=0 and |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 then find the value of x