If p-3-5- q-2-7-5-m - r-3-2-n and hcf-q-r- - 2-3-x and HCF-p-q- -5 then find the values of m - n and x respectively-

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Highest Common Factors

if p=3⁴×5², q...

Question

if p=3⁴×5², q=2⁴×7×5^m , r=3⁸×2^n and hcf(q,r) = 2³×3^x and HCF(p,q) =5 then find the values of m , n and x respectively.

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{(1 + x + x^{2})}^{n} = 2 n \sum r = 0 a_{r} x^{r} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a^{2 n} x^{2 n}

P = a_{0} + a_{3} + a_{6} + . . .

Q = a_{1} + a_{4} + a_{7} + . . .

R = a_{2} + a_{5} + a_{8} + . . .

P, Q, R

\frac{3 m + 2 n}{q + p} - \frac{4 p - 3 n}{q + r} + \frac{2 p + 3 m}{q + m}

n \times n

det (P^{2} {QR}^{- 1}) .

n \times n

det (P^{2} {QR}^{- 1}) .

If a = 2^p × 3^q × 5^r and b = p^2 × q^3 × r^5 , where p, q and r are primes, find the value of p + q + r, given that a = b.

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