How do you solve the equation #sqrtt+sqrt(1+t)-4=0# to find the zeros of the given function?

Answer 1

#t = (15/8)^2#

First we establish the feasible solutions. They must obey:

From #sqrt(t)->t ge 0# and from #sqrt(1+t)->1+t ge 0# so #t ge 0#

Now grouping

#sqrt(t+1) = 4 - sqrt(t)#

and squaring

#t+1=16-8sqrt(t)+t# simplifying
#8sqrt(t)=15# so
#t = (15/8)^2 > 0#

so the solution is feasible

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Answer 2

To solve the equation sqrt(t) + sqrt(1+t) - 4 = 0, we can follow these steps:

  1. Start by isolating one of the square root terms. Subtract sqrt(1+t) from both sides of the equation: sqrt(t) = 4 - sqrt(1+t)

  2. Square both sides of the equation to eliminate the square root: (sqrt(t))^2 = (4 - sqrt(1+t))^2 t = (4 - sqrt(1+t))^2

  3. Expand the right side of the equation: t = 16 - 8sqrt(1+t) + (1+t)

  4. Simplify the equation: t = 17 + t - 8sqrt(1+t)

  5. Rearrange the equation to isolate the square root term: 8sqrt(1+t) = 17

  6. Square both sides of the equation to eliminate the square root: (8sqrt(1+t))^2 = 17^2 64(1+t) = 289

  7. Expand and simplify the equation: 64 + 64t = 289

  8. Rearrange the equation to isolate the variable: 64t = 289 - 64 64t = 225

  9. Divide both sides of the equation by 64: t = 225/64

Therefore, the solution to the equation sqrt(t) + sqrt(1+t) - 4 = 0 is t = 225/64.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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