Question

If 2,x 242 y 2 are in G.p find the value of x,y and 2

Answer 1

Step-by-step explanation:

it is in G.P

so let,

t2/t1 = x/2 eq(1)

t3/t2 = 242/x eq(2)

t4/t3 = y/242 eq(3)

t5/t4 = 2/y eq(4)

now,

take (1) = (2)

=>x/2 = 242/ x

=>x^2 = 484 (using cross multiplication)

taking square root on both sides

we get:

x = 22 eq(5)

now take (3) = (4)

=>y/242 = 2/y

=> y×y = 2×242 ( using cross multiplication )

=> y^2 = 484

taking square root on both sides, gives

=> y= 22 eq(6)

lastlly forbvalue of 2

take (4) = (1)

=> 2/y = x/2

take y divided on L.H.S to R.H.S ithen it gets multiplied there.

=> 2 = x/2 × y

now putting the value of x,y from eq(5) , eq(6)

in above equation.

=> 2 = 22/2×22

=!>2= 242