Question
Evaluate:
(28)3 + (-15)3 + (-13)3
(28)3 + (-15)3 + (-13)3
✓
Answer
(28)3 + (-15)3 + (-13)3
We know:
x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - zx)
x3 + y3 + z3 = (x + y + z)(x2 + y2 + z2 - xy - yz - zx) + 3xyz
Here, x = (-28), y = -15, z = -13
(28)3 + (-15)3 + (-13)3
= (28 - 15 - 13)[(28)2 + (-15)2 + (-13)2 - 28(-15) - (-15)(-13) - 28(-13)] + 3 × 28(-15)(-13)
= 0 + 16380
= 16380
We know:
x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - zx)
x3 + y3 + z3 = (x + y + z)(x2 + y2 + z2 - xy - yz - zx) + 3xyz
Here, x = (-28), y = -15, z = -13
(28)3 + (-15)3 + (-13)3
= (28 - 15 - 13)[(28)2 + (-15)2 + (-13)2 - 28(-15) - (-15)(-13) - 28(-13)] + 3 × 28(-15)(-13)
= 0 + 16380
= 16380
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.
Prove that in a quadrilateral the sum of all the sides is geater than the sum of its diagonals.
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallels to BC intersects AC at D.Show that :
→- D is the mid-point of AC
- MD $\perp$ AC
- CM = MA = $\frac{1}{2}$AB
ABC is a triangle in which $\angle\text{A}=72^\circ,$ the internal bisectors of angles B and C meet in O. Find the magnitude of $\angle\text{BOC}.$
→Find the area of a triangle whose sides are respectively 150cm, 120cm and 200cm.
Draw the graphs of the following linear equations on the same graph paper:
2x + 3y = 12, x - y = 1
Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also, find the area of the triangle.
2x + 3y = 12, x - y = 1
Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also, find the area of the triangle.
Plot the following points on the graph paper:
(-4, 0)
In figure, O is the centre of the circle. If $\angle\text{APB}=50^\circ,$ find $\angle\text{AOB}$ and $\angle\text{OAB}.$
→If the angles A, B and C of $\triangle\text{ABC}$ satisfy the relation B − A = C − B, then find the measure of $\angle\text{B}.$
→ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of $\triangle\text{PQR}$ is double the perimeter of $\triangle\text{ABC}.$
→