Question

$verify x = \frac{3}{4} \: \: y = \frac{5}{6} \: \: z = \frac{ - 7}{8}$
explain required ​

Answer 1

Step-by-step explanation:

Answer

(i) [

4

x

3

5

]=[

y

1

z

5

]

As the given matrices are equal, their corresponding elements are also equal.

Comparing the corresponding elements, we get: x=1,y=4, and z=3

(ii) [

x+y

5+z

2

xy

]=[

6

5

2

8

]

As the given matrices are equal, their corresponding elements are also equal. Comparing the corresponding elements, we get:

x+y=6,xy=8,5+z=5

Now, 5+z=5⇒z=0

We know that:

(x−y)

2

=(x+y)

2

−4xy

⇒(x−y)

2

=36−32=4

⇒x−y=±2

Now, when x−y=2 and x+y=6, we get x=4 and y=2

When x−y=−2 and x+y=6, we get x=2 and y=4

∴x=4,y=2 and z=0orx=2,y=4 and z=0

Answer 2

GIVEN

$verify x = \frac{3}{4} \: \: y = \frac{5}{6} \: \: z = \frac{ - 7}{8}$

TO FIND:-

• required solutions

EXPLAIN:-

$x = (y + z) = (x + y) + z \\ \\ x = (y + z) = \frac{3}{4} + ( \frac{5}{6} + \frac{ - 7}{8} ) \\ \\ = \frac{3}{4} + ( \frac{20 + ( - 21)}{24} ) \\ \\ = \frac{3}{4} + ( \frac{ - 1}{24} ) \\ \\ = \frac{3}{4} + \frac{ - 1}{24} \\ \\ = \frac{18 + ( - 1)}{24} \\ \\ = \frac{17}{24} \\ \\ (x + y ) + z = ( \frac{3}{4} + \frac{5}{6} ) + \frac{ - 7}{8} \\ \\ = ( \frac{9 + 10}{12} ) + \frac{ - 7}{8} \\ \\ = \frac{19}{12} + \frac{ - 7}{8} \\ \\ = \frac{38 + ( - 21)}{24} \\ \\ = \frac{38 - 21}{24} \\ \\ = \frac{17}{24} \\ \\ x + (y + z) = (x + y) + z$

•°• verified