Question

Find y in the following i) 2 x ( -6 + y) = 2 x (-6) + 2 x 10​

Answer 1

Answer:

=> [(2k+1)(3)^(k+1+1)+3]/4

=> [(2k+1)(3)^(k+2)+3]/4

LHS = RHS is true for n=k+1

The result is true for n=k+1

This result is true for all positive integers for n.

Hence, Proved.

Used formulae:

a^m x a^n = a^(m+n) (a^m)^n = a^(mn)

Used Method:

Mathematical Induction.

Answer 2

Answer:

2x+y=6

⟹y=6−2x

Let, x=1, then y=6−2(1)=4

Similarly, when x=2,y=2

x−2y+2=0

⟹x=2y−2

Let, y=0, then x=2(0)−2=−2

Similarly, when y=2,x=2

Plotting the above points on the graph, we get, the vertices of the traingle, i.e. A(2,3),B(3,0),C(−2,0)

∴ Area of the triangle =

2

1

×5units×2units

=5 sq. units