if vertices of equilateral triangle lies on curve is 8x^3+y^3+6xy=1 then side length and area of triangle is
Answers
Answer:
8x³ +y³ +6xy =1
Factorise the above equation
(2x)³+(y)³+(-1)³ = 3(2x)(y)(-1)
Using property [ a³+b³+c³ =3abc ]
=> (2x +y -1 )(4x²+y²+1-2xy+ y+ 2x)
Hence
Edge length of ∆ = 6/√15
Area = 3√3/5
Step-by-step explanation:
Answer:
The edge length = 6/15.
Area = 3√3/5.
Step-by-step explanation:
8x³ +y³ +6xy =1
Factorize the equation above.
(2x)³+(y)³+(-1)³ = 3(2x)(y)(-1)
Using the formula [a3+b3+c3 = 3abc]
=> (2x +y -1 )(4x²+y²+1-2xy+ y+ 2x)
Hence
The edge length is 6/15.
Area is 3√3/5.
Additional Information:
In general, l2=12(a2+b2+c2+23), where is the area of a triangle with side a, b, and c, if a point inside an equilateral triangle with side l is distanced from the three vertices by a, b, and c.
You must apply the coordinate geometry formula to determine the area of a triangle where you know the x and y coordinates of the three vertices: area is equal to Ax(By - Cy), Bx(Cy - Ay), and Cx(Ay - By) in absolute value, divided by 2.
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