Question

Solve the following questions step by step​

Answer 1

1. Value of determinant= ad-bc= 3√6 x 2 -(-4√2)5√3= 6√6+20√6= 26√6----(Ans)

2. Let 1/3x-2= a   and     1/4y+3= b

8a+45b=5                           12a-30b=1

24a+135b=15                       24b-60b=2

Subtracting,

195 b=13

b=13/195=1/15

a= 15-135b/2a= 15-9/24=6/24=1/4

3x-2=4            4y+3=15

3x=6                 4y=12

x=2                    y=3

3. Let it be the nth term.

Now,

a+(n-1)d=aₙ

3+(n-1)8=547

(n-1)8=544

n-1=544/8=68

n=69

Thus it is the 69th term.

4.Let the terms be a-d,a,a+d

Now,

a-d+a+a+d=30

3a=30

a=10

(a-d)a(a+d)=360

(10-d)(10+d)10=360

100-d²=36

d²=64

d=±8

Terms: 2,10,18 or 18,10,2

5. 2x²+x-1/5=0

Multiplying both sides by 5,

10x²+x-1=0

By formula,

x= -1±√(1)²-4(10)(-1) / 20

x= -1±√41 /20