If the line y-x cuts the curve x3-3y3-30xy-72x-55-0 in points A-B and C then the value of 4-255 OA-OB-OC where O is the origin - is -

The correct option is D 4 x ^ 3 +3 y ^ 3 30xy+72x 55=0 y=x ⇒ x ^ 3 +3 x ^ 3 30 x ^ 2 +72x 55=0 ⇒ 4 x ^ 3 30 x ^ 2 +72x 55=0 ⇒ ...

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Byju's Answer

Standard XII

Mathematics

Properties of Set Operation

If the line ...

Question

If the line $y = x$ cuts the curve $x^{3} + {3 y}^{3} - 30 x y + 72 x - 55 = 0$ in points $A, B$ and $C$ then the value of $\frac{4 \sqrt{2}}{55}$ $O A . O B . O C$ (where $O$ is the origin ), is ?

55

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\frac{1}{4 \sqrt{2}}

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2

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4

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Solution

The correct option is D $4$
$x^{3} + 3 y^{3} - 30 x y + 72 x - 55 = 0$
$y = x$
$\Rightarrow x^{3} + 3 x^{3} - 30 x^{2} + 72 x - 55 = 0$
$\Rightarrow 4 x^{3} - 30 x^{2} + 72 x - 55 = 0$
$\Rightarrow x = 1.634, - 3.367, 2.5$
$∴ A (1.634, 1.634); B (3.367, 3.367); C (2.5, 2.5)$
$O A = 1.634 \sqrt{2}, O B = 3.367 \sqrt{2}, O C = 2.5 \sqrt{2}$
$= \frac{4 \sqrt{2}}{55} \times O A \times O B \times O C = 4$

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If the line y=x cuts the curve x3+3y3−30xy+72x−55=0 in points A,B and C then the value of 4√255 OA.OB.OC (where O is the origin ), is ?

The correct option is D 4x3+3y3−30xy+72x−55=0y=x⇒x3+3x3−30x2+72x−55=0⇒4x3−30x2+72x−55=0⇒x=1.634,−3.367,2.5∴A(1.634,1.634);B(3.367,3.367);C(2.5,2.5)OA=1.634√2,OB=3.367√2,OC=2.5√2=4√255×OA×OB×OC=4

If the line $y = x$ cuts the curve $x^{3} + {3 y}^{3} - 30 x y + 72 x - 55 = 0$ in points $A, B$ and $C$ then the value of $\frac{4 \sqrt{2}}{55}$ $O A . O B . O C$ (where $O$ is the origin ), is ?