Question

Answer this with step by step explanation...
.
.
chapter- Rational numbers​

Answer 1

Given:

• x = 1/2
• y = 2/3
• z = -1/5

To prove:

(x + y) + z = x + (y + z)

Solution:

For LHS;

First, find out (x + y)

$\bf{\dfrac{1}{2}+\dfrac{2}{3}}$

$\hookrightarrow \: \sf{\dfrac{3+4}{6}}$

$= \: \sf{\dfrac{7}{6}}$

Now add this to 'z'

$\bf{\dfrac{7}{6}-\dfrac{1}{5}}$

$= \: \sf{\dfrac{35-6}{30}}$

$= \: \boxed{\sf{\dfrac{29}{30}}}$

Now for RHS

First, find out (y + z)

$\bf{\dfrac{2}{3}-\dfrac{1}{5}}$

$= \: \sf{\dfrac{10-3}{15}}$

$= \: \sf{\dfrac{7}{15}}$

Add this to 'x'

$\bf{\dfrac{7}{15}+\dfrac{1}{2}}$

$= \: \sf{\dfrac{14+15}{30}}$

$= \: \boxed{\sf{\dfrac{29}{30}}}$

As we can observe, LHS = RHS

⍟ HENCE VERIFIED ⍟

Answer 2

Answer:

A partial differential equation (or briefly a PDE) is a mathematical equation that involves two or more independent variables, an unknown function (dependent on those variables), and partial derivatives of the unknown function with respect to the independent variables.