CameraIcon

SearchIcon

MyQuestionIcon

1

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

Property 6

If x=3+3 1/...

Question

If $x = 3 + 3^{1 / 3} + 3^{2 / 3}$ then $x^{3} - 9 x^{2} + 18 x =$

A

0

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

B

12

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

C

- 12

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

D

- 24

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

Open in App

Solution

The correct option is B $12$
question given
$x = 3 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}$ - (1) find $x^{3} - 9 x^{2} + 18 x$
$(x - 3) = 3^{\frac{1}{3}} + 3^{\frac{2}{3}}$
therefore , cube both sides
$(x - 3)^{3} = (3^{\frac{1}{3}} + 3^{\frac{2}{3}})^{3}$ $(a - b)^{3} = a^{3} + b^{3} - 3 a b (a + b)$
$(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$x^{3} - 27 - 9 x^{2} + 27 x = 3 + 9 + 3 \times 3 (3^{\frac{1}{3}} + 3^{\frac{2}{3}})$
put (x-3)= $3^{\frac{1}{3}} + 3^{\frac{2}{3}}$
$x^{3} - 27 - 9 x^{2} + 27 x = 12 + 9 (x - 3)$
$x^{3} - 27 - 9 x^{2} + 27 x = 12 + 9 x - 27$
$x^{3} - 27 + 9 x^{2} + 27 x - 12 - 9 x + 27 = 0$
$x^{3} - 9 x^{2} + 18 x - 12 = 0$
$x^{3} - 9 x^{2} + 18 x = 12$

Suggest Corrections

thumbs-up

0

Similar questions

x = 3 + 3^{1 / 3} + 3^{2 / 3}

x^{3} - 9 x^{2} + 18 x - 12

=

x = 3 + 3^{\frac{1}{2}} + 3^{\frac{2}{3}}

x^{3} - 9 x^{2} + 18 x - 12

x = 3 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}

, then find the value of

x^{3} - 9 x^{2} + 18 x

If [x=3+3^(1/3)+3^(2/3)] , then prove that [(x^3)-(9x^2)+18x-12]=0

y = x^{4} + x^{3} - 18 x^{2} + 24 x - 12

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Laws of Logarithm with Use

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon