61-303 - 5-63 -6-53 is equal to

(61/30)^3 (5/6)^3 (6/5)^3 = [(6/5)^3 +(5/6)^3]^3 (6/5)^3 (5/6)^3 nbsp; = (6/5)^3 +(5/6)^3 + 3(6/5)(5/6)(6/5+5/6) (6/5)^3 (5/6)^3 = 3(6/5+5/6) = 3 ×(36+ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Algebraic Identities

61/303 - 5/63...

Question

$(\frac{61}{30})^{3} - (\frac{5}{6})^{3} - (\frac{6}{5})^{3}$ is equal to

\frac{16}{15}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{61}{10}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{5}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{61}{90}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{61}{10}$

$(\frac{61}{30})^{3} - (\frac{5}{6})^{3} - (\frac{6}{5})^{3}$
$= [(\frac{6}{5})^{3} + (\frac{5}{6})^{3}]^{3} - (\frac{6}{5})^{3} - (\frac{5}{6})^{3}$
$= (\frac{6}{5})^{3} + (\frac{5}{6})^{3} + 3 (\frac{6}{5}) (\frac{5}{6}) (\frac{6}{5} + \frac{5}{6}) - (\frac{6}{5})^{3} - (\frac{5}{6})^{3}$
$= 3 (\frac{6}{5} + \frac{5}{6})$
$= 3 \times \frac{(36 + 25)}{30}$
$= \frac{61}{10}$
Hence, the correct answer is option (2).

Suggest Corrections

Similar questions

Q. The sum of the series

\frac{30}{(6 - 5) (6^{2} - 5^{2})} + \frac{30^{2}}{(6^{2} - 5^{2}) (6^{3} - 5^{3})} + \frac{30^{3}}{(6^{3} - 5^{3}) (6^{4} - 5^{4})} + \dots \infty

Q. Given that 1 + 2 + 3 + 4 + 5 + 6 = 21, the sum of 61 + 62 + 63 + 64 + 65 + 66 is .

\frac{5^{n + 2} - 6 \times 5^{n + 1}}{13 \times 5^{n} - 2 \times 5^{n + 1}}

is equal to

(a)

\frac{5}{3}

(b)

- \frac{5}{3}

(c)

\frac{3}{5}

(d)

- \frac{3}{5}

Q. The value of the infinite product

6^{\frac{1}{2}} \times 6^{\frac{1}{2}} \times 6^{\frac{3}{8}} \times 6^{\frac{1}{4}} \times . . . . . . . . .

Multiply and express as a mixed fraction:

(a) (b)

(e) (f)

Join BYJU'S Learning Program

(6130)3−(56)3−(65)3 is equal to

The correct option is B 6110 (6130)3−(56)3−(65)3 =[(65)3+(56)3]3−(65)3−(56)3 =(65)3+(56)3+3(65)(56)(65+56)−(65)3−(56)3 =3(65+56) =3×(36+25)30 =6110 Hence, the correct answer is option (2).

$(\frac{61}{30})^{3} - (\frac{5}{6})^{3} - (\frac{6}{5})^{3}$ is equal to