Question

If the distance between the points (t, t) and (4, 5) is (t - 3) units, then the value of t can be​

Answer 1

Answer:

t=8 , 4

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Answer 2

Answer:

Required value of t is 8 or 4.

Step-by-step explanation:

Given, distance between (t, t) and (4, 5) is (t - 3).

For solving this problem we should know what is the distance formula of two points ?

Let,(a,b) and (c,d) be two points.

Therefore distance between them

$\sqrt{ {(a - c)}^{2} + {(b - d)}^{2} }$

unit .

Here

$a = t \\ b = t\\ c = 4 \\ d = 5$

So, distance between (t,t) and (4,5) is

$\sqrt{ {(t - 4)}^{2} + {(t - 5)}^{2} }$

According to question,

$\sqrt{ {(t - 4)}^{2} + {(t - 5)}^{2} } = t - 3$

${(t - 4)}^{2} + {(t - 5)}^{2} = {(t - 3)}^{2}$

${t}^{2} - 8t + {4}^{2} + {t}^{2} - 10t + {5}^{2} = {t}^{2} - 6t + {3}^{2}$

${t}^{2} - 8t + 16 + {t}^{2} - 10t + 25 = {t}^{2} - 6t + 9$

${t}^{2} + {t}^{2} - {t}^{2} - 8t - 10t + 6t = 9 - 16 - 25$

${t}^{2} - 12t = 32$

${t}^{2} - 12t - 32 = 0$

${t}^{2} - (8 + 4)t - 32 = 0 \\ {t}^{2} - 8t - 4t - 32 = 0 \\ t(t - 8) - 4(t - 8) = 0 \\ (t - 8)(t - 4) = 0$

Product of term is zero then they are separately zero.

$t - 8 = 0 \\ t = 8$

and

$t - 4 = 0 \\ t = 4$

Here applied formula,

${(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

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2) https://brainly.in/question/1169549