Question

i) Solve the following equation if x >= 0 ((5x + 2) ^ 2 + (5x - 2) ^ 2)/((5x + 2) ^ 2 - (5x - 2) ^ 2) = 13/12​

Answer 1

Answer:

Correct option is

A

0.6

Given

(5x+2)

2

−(5x−2)

2

(5x+2)

2

+(5x−2)

2

=

12

13

Applying the formulae, (a+b)

2

+(a−b)

2

=2(a

2

+b

2

)

and (a+b)

2

−(a−b)

2

=4ab where a=5x;b=2

4×(5x)×2

2((5x)

2

+2

2

)

=

12

13

20x

25x

2

+4

=

12

13

On cross multiplying and simplifying,

75x

2

−65x+12=0

75x

2

−20x−45x+12=0

5x(15x−4)−3(15x−4)=0

(5x−3)(15x−4)=

x={

5

3

,

15

4

}={0.6,0.27}

Hence, m=0.6