MyQuestionIcon

1

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

Geometric Progression

Simplify:155×...

Question

Simplify:
$\frac{155 \times 155 \times 155 - 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55}$

Open in App

Solution

Given $\frac{155 \times 155 \times 155 - 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55}$

$∴ \frac{155 \times 155 \times 155 - 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55}$
$= \frac{(155)^{3} - (55)^{3}}{(155)^{2} + 155 \times 55 + (55)^{2}}$
$= \frac{(155 - 55) [(155)^{2} + 155 \times 55 + (55)^{2}]}{(155)^{2} + 155 \times 55 + (55)^{2}}$
$[∴ a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})]$
$= 155 - 55$
$= 100$

Hence, $\frac{155 \times 155 \times 155 - 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55} = 100$

Suggest Corrections

thumbs-up

2

Similar questions

Q. Simplify:

(i)

\frac{173 \times 173 \times 173 + 127 \times 127 \times 127}{173 \times 173 - 173 \times 127 + 127 \times 127}

\frac{155 \times 155 \times 155 - 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55}

\frac{1.2 \times 1.2 \times 1.2 - 0.2 \times 0.2 \times 0.2}{1.2 \times 1.2 + 1.2 \times 0.2 + 0.2 \times 0.2}

Simplify: $\frac{[155 \times 155 \times 155 - 55 \times 55 \times 55]}{[155 \times 155 + 155 \times 55 + 55 \times 55]}$

Q. Simplify:

(i)

\frac{173 \times 173 \times 173 + 127 \times 127 \times 127}{173 \times 173 - 173 \times 127 + 127 \times 127}

\frac{155 \times 155 \times 155 - 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55}

\frac{1.2 \times 1.2 \times 1.2 - 0.2 \times 0.2 \times 0.2}{1.2 \times 1.2 + 1.2 \times 0.2 + 0.2 \times 0.2}

Q. In the figure, ABCD and AEFG are parallelograms. If

∠ C = 55^{\circ}

, what is the measure of

∠ E

Q. Angles subtended by chords

A C

B C

O

of the circle are

55^{o}

155^{o}

respectively. What is the measure of

∠ A C B

?

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Geometric Progression

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon