sqrt[3]{61 - 46sqrt{5}} = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $\sqrt[3]{61 - 46\sqrt{5}} = a - b\sqrt{5}$.Then,$61 - 46\sqrt{5} = (a - b\sqrt{5})^3$.Using the identity $(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y

Vedclass · Accepted Answer

$1 - 2\sqrt{5}$

Vedclass · Answer

(A) Let $\sqrt[3]{61 - 46\sqrt{5}} = a - b\sqrt{5}$.Then,$61 - 46\sqrt{5} = (a - b\sqrt{5})^3$.Using the identity $(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3$,we get:$61 - 46\sqrt{5} = a^3 - 3(a^2)(b\sqrt{5}) + 3(a)(b\sqrt{5})^2 - (b\sqrt{5})^3$$61 - 46\sqrt{5} = a^3 - 3a^2b\sqrt{5} + 15ab^2 - 5b^3\sqrt{5}$$61 - 46\sqrt{5} = (a^3 + 15ab^2) - (3a^2b + 5b^3)\sqrt{5}$.Comparing rational and irrational parts:$a^3 + 15ab^2 = 61$ and $3a^2b + 5b^3 = 46$.If we test $a = 1$ and $b = 2$:$1^3 + 15(1)(2^2) = 1 + 60 = 61$ (Matches).$3(1^2)(2) + 5(2^3) = 6 + 40 = 46$ (Matches).Thus,$\sqrt[3]{61 - 46\sqrt{5}} = 1 - 2\sqrt{5}$.

$\sqrt[3]{61 - 46\sqrt{5}} = $

Similar Questions

In India,electricity is supplied for domestic use at $220 \,V$. It is supplied at $110 \,V$ in the $USA$. If the resistance of a $60 \,W$ bulb for use in India is $R$,what will be the resistance of a $60 \,W$ bulb for use in the $USA$?

$A$ particle of charge $q$ and mass $m$ moves in a circular orbit of radius $r$ with angular speed $\omega$. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

When an unpolarized light of intensity $I_0$ is incident on a polarizing sheet,the intensity of the light which does not get transmitted is

If $\alpha, \beta$ and $\gamma$ are the lengths of the altitudes of a $\triangle ABC$ with area $\Delta$,then $\frac{\Delta^2}{R^2}\left(\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2}\right)$ is equal to

Water is pumped from a depth of $10\, m$ and delivered through a pipe of cross section $10^{-2}\, m^2$. If it is needed to deliver a volume of $10^{-1}\, m^3$ per second,the power required will be: ............ $kW$

Vedclass Test Series

Exam Paper Generator

Online Exam Module