Discussion Topic

Solving equations involving real values of t

Summary:

Solving equations involving real values of \( t \) generally requires isolating \( t \) by performing algebraic operations such as addition, subtraction, multiplication, division, and using functions like square roots or logarithms. The specific steps depend on the equation's form, but the goal is to express \( t \) in terms of other known quantities, ensuring all operations are valid for real numbers.

Expert Answers

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Solve for real t 11^(t+1) -1=4*11^t

We have to solve 11^(t+1) -1=4*11^t for t.

11^(t+1) -1=4*11^t

=> 11^t*11 - 1 = 4*11^t

let 11^t = x

=> 11x - 1 = 4x

=> 7x = 1

=> x= 1/7

11^t = 1/7

Here the bases are different, so we have to use the log function.

log 11^t = log (1/7)

=> t* log 11 = -log 7

=> t = -log 7 / log 11

The required value of t is -log 7 / log 11

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Solve the equation t^4+10t-11=0

It is not possible to solve the equation you have given t^4 + 10t - 11 = 0.

Instead, here is the solution for t^4 + 10 t^2 - 11 = 0

let t^2 = x

=> x^2 + 10x - 11 = 0

=> x^2 + 11x - x - 11 = 0

=> x(x + 11) - 1(x + 11) = 0

=> (x - 1)(x + 11) = 0

=> x = 1 and x = -11

t^2 = 1

=> t1 = 1

=> t2 = -1

t^2 = -11

=> t3 = i*sqrt 11

=> t4 = -i*sqrt 11

The solutions of the equation t^4 + 10 t^2 - 11 = 0 are {-1 , 1, i*sqrt 11, -i*sqrt 11}

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