Math, asked by unknownguy4999, 11 months ago

If pqr=a^(x) qrs=a^(y) and rsp=a^(z) then find the value of (pqrs) 1/2

Answers

Answered by abhi178
15

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}

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