Let a be a positive real number, and let m and n be positive integers such that

Question

Let a be a positive real number, and let m and n be positive integers such that m n. Find, in terms of a, m, and n, a positive real number x such that the ratio of a^(1/m) (supposed to be the squareroot form) to x is equivalent to the ratio of x to a^(1/n) (supposed to be the squareroot form) Let a be a positive real number, and let m and n be positive integers such that m n. Find, in terms of a, m, and n, a positive real number x such that the ratio of a^(1/m) (supposed to be the squareroot form) to x is equivalent to the ratio of x to a^(1/n) (supposed to be the squareroot form)

Explanation / Answer

We have a1/m/x = x/a1/n . On multiplying both the sides by a1/n/x, we get (a1/m/x)( a1/n/x) = (x/a1/n)( a1/n/x) or, [(a1/m)(a1/n)]/x2 =1 or, x2 = a(1/m+1/n) or, x2 = a(m+n)/mn . Then,on taking square roots of both the sides, we get x = ± a(m+n)/2mn

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.