How do you solve the equation #sqrtt+sqrt(1+t)-4=0# to find the zeros of the given function?
First we establish the feasible solutions. They must obey:
Now grouping
and squaring
so the solution is feasible
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To solve the equation sqrt(t) + sqrt(1+t) - 4 = 0, we can follow these steps:
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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)
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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
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Expand the right side of the equation: t = 16 - 8sqrt(1+t) + (1+t)
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Simplify the equation: t = 17 + t - 8sqrt(1+t)
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Rearrange the equation to isolate the square root term: 8sqrt(1+t) = 17
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Square both sides of the equation to eliminate the square root: (8sqrt(1+t))^2 = 17^2 64(1+t) = 289
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Expand and simplify the equation: 64 + 64t = 289
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Rearrange the equation to isolate the variable: 64t = 289 - 64 64t = 225
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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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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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