if p(2n – 1, n) : p(2n + 1, n – 1) = 22 : 7 find n.
if p(2n – 1, n) : p(2n + 1, n – 1) = 22 : 7 find n.
given: p(2n – 1, n) : p(2n + 1, n – 1) = 22 : 7to find: value of nwe know,so, according to question:p(2n – 1, n) : p(2n + 1, n – 1) = 22 : 7⇒ 7(n + 2)(n + 1) = 22×2 (2n + 1)⇒ 7(n2 + n + 2n + 2) = 88n + 44⇒ 7(n2 + 3n + 2) = 88n + 44⇒ 7n2 + 21n + 14 = 88n + 44⇒ 7n2 + 21n – 88n + 14 – 44 = 0⇒ 7n2 – 67n – 30 = 0⇒ 7n2 – 70n + 3n – 30 = 0⇒ 7n(n – 10) + 3(n – 10) = 0⇒ (n – 10)(7n + 3) = 0∴ the value of n = 10
given: p(2n – 1, n) : p(2n + 1, n – 1) = 22 : 7to find: value of nwe know,so, according to question:p(2n – 1, n) : p(2n + 1, n – 1) = 22 : 7⇒ 7(n + 2)(n + 1) = 22×2 (2n + 1)⇒ 7(n2 + n + 2n + 2) = 88n + 44⇒ 7(n2 + 3n + 2) = 88n + 44⇒ 7n2 + 21n + 14 = 88n + 44⇒ 7n2 + 21n – 88n + 14 – 44 = 0⇒ 7n2 – 67n – 30 = 0⇒ 7n2 – 70n + 3n – 30 = 0⇒ 7n(n – 10) + 3(n – 10) = 0⇒ (n – 10)(7n + 3) = 0∴ the value of n = 10