If pqr=a^(x) qrs=a^(y) and rsp=a^(z) then find the value of (pqrs) 1/2
Answers
Given : pqr = a^x .........(1)
qrs = a^y ...........(2)
and rsp = a^z .........(3)
here you can see that p, q, r and s are four variable terms but you have given only three equations. to get (pqrs)½ , we need one more equation.
i.e., spq = a^w [ let] .......(4)
To find : The value of (pqrs)½
solution : multiplying equations (1), (2) (3) and (4) we get,
(pqr) × (qrs) × (rsp) × (spq) = a^x × a^y × a^z
⇒(p³q³r³s³) = a^(x + y + z + w)
⇒(pqrs)³ = a^(x + y + z + w)
⇒(pqrs) = a^{(x + y + z + w)/3}
⇒(pqrs)½ = a^{(x + y + z + w)/6}
Therefore the value of (pqrs)½ is a^{(x + y + z + w)/6}
also read similar questions : In triangle pqr base qr is divided at x such that qx=1/2xr. If area of triangle pqr=81cm^2, find area of triangle pqx.
https://brainly.in/question/1096049
∆ LMN ~ ∆PQR, 9 × A (∆PQR) = 16 × A (∆LMN). If QR =20 then find MN.
https://brainly.in/question/3860152