Question

If three points a(6,2),b(4,0) and c(α,β)a(6,2),b(4,0) and c(α,β) are such that (|ac+cb|+|ac−cb|)(|ac+cb|+|ac−cb|) is minimum, then the value of (α+β)(α+β) is equal to

Answer 1

Answer:

Step-by-step explanation:

Step-by-step explanation:

CSA = 32 m sq

= 2(l + b) h = 32

= (l + b) h = 16

TSA = 86 m sq

= 2(lb + bh + lh) = 86

= (lb + bh + lh) = 43

= lb + h(l+b) = 43

= lb + 16 = 43

lb = 43 - 16 = 27

lb = 27

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Answer 2

Concept:

A linear equation is a straight line equation. Based on known variables, angles, and constants, a straight line on a cartesian plane can have various representations. The direction of a straight line is determined by the slope of the line.

Given:

The points $A(6,2), B(4,0)$ and $C(\alpha ,\beta )$. The value of $(|AC+CB|+|AC-CB|)$ is minimum.

Find:

The value of $(\alpha + \beta)$.

Solution:

$|AC+BC|\geq |AB|\\|AC+BC|\geq \sqrt{(6-4)^2+(2-0)^2}\\ |AC+BC|\geq \sqrt{4+4} \\ |AC+BC|\geq 2\sqrt{2}$

$|AC-BC|\leq AB\\AC-BC=0\\AC=BC$

$C$ is the mid-point of $AB$.

Point  $C$ is $\frac{6+4}{2},\frac{2+0}{2}$ $= (5,1)$

The value of $\alpha$ is $5$ and the value of $\beta$ is $1$.

The value of $\alpha +\beta$ is $6$.

Hence, the value of  $\alpha +\beta$ is $6$.