Question

plz solve this question

Answer 1

Answer:The value of A is 45° and the value of B is 15°.

Step-by-step explanation:

Tan(A+B)=√3

Tan(A-B)=1/√3

But we know tan60°=√3 and tan30°=1/√3.

Therefore,

Tan(A+B)=60°  ----(1)

Tan(A-B)=30°   ----(2)

Adding (1) and (2),

2A=90°

A=45°

Using A=45° in (1),

45°+B=60°

B=15°.

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Thank you.

Answer 2

2(x^2 + 1/x^2) - 9(x + 1/x) + 14=0

use identity: a^2 + b^2 = (a + b)^2 - 2ab

so then

(x^2 + 1/x^2) = (x + 1/x)^2 - 2(x)(1/x)

= (x + 1/x)^2 - 2

now

2[(x + 1/x)2 - 2] -9(x +1/x) +14=0

2(x +1/x)^2 - 4 - 9(x + 1/x) + 14=0

2(x + 1/x)^2 - 9(x + 1/x) + 10 =0

let (x + 1/x) = p

2p^2 - 9p + 10= 0

2p^2 - 4p - 5p + 10=0

2p(p - 2) - 5(p - 2) =0

(p-2) (2p - 5) = 0

p = 2 , 5/ 2

when p = 2

x + 1/x = 2 => x^2 + 1 = 2x

x^2 +1 - 2x = 0

x^2 +2 -1 - 2x=0

(x -1) (x -1) = 0

(x - 1)^2 = 0

x - 1 = 0 => x = 1 ans.

when p = 5/2

then x + 1/x = 5/2

2x^2 + 2 = 5x => 2x^2 - 5x + 2 =0

2x^2 - 4x - x + 2= 0

2x( x - 2) -1 (x - 2) = 0

(2x - 1) (x - 2) = 0

x = 1/2 , x = 2

hence, possible values of x

are 1, 1/2 and 2.

Answer: x = 1, 1/2, 2