Question

Express x in terms of y and b when y = √(ax - b).

Additionally, determine the value of k if k√28 + √63 - √7 = 0.

Answer 1

To express x in terms of y and b when y = √(ax - b), the expression (y^2 + b)/a can be used. The value of k can be determined as (√7 - √63)/√28.

Step-by-step explanation:

To express x in terms of y and b when y = √(ax - b), we can rearrange the equation and isolate x:

y = √(ax - b)

Squaring both sides of the equation, we get:

y^2 = ax - b

Adding b to both sides, we get:

y^2 + b = ax

Dividing both sides by a, we get:

x = (y^2 + b)/a

So x can be expressed in terms of y and b as (y^2 + b)/a.

For the second part of the question, to determine the value of k if k√28 + √63 - √7 = 0, we can rearrange the equation:

k√28 = √7 - √63

Dividing both sides by √28, we get:

k = (√7 - √63)/√28

Answer 2

`\sf x = (y^2+b)/(a)\\\\\\k = -1`

Step-by-step explanation:

Express x in terms of y and b:

• Take square root both sides,

`\sf (√(ax -b))^2=y^2\\\\ax - b = y^2`

• Now, add 'b' to both sides,

ax = y² + b

• Divide both sides by 'a',

`\sf (ax)/(a)=(y^2+ b)/(a)\\\\\\~~x = (y^2+b)/(a)`

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`k√(28) + √(63)-√(7)` = 0

To determine 'k', simplify the radicals.

`\sf k √(2*2*7)+√(3*3*7)-√(7)=0\\\\~~~~~~~~~~~~k*2√(7)+3√(7)-√(7)=0\\\\~~~~~~~~~~~~~~~`

`\sf 2k√(7) + 2√(7)=0\\\\`

`\sf 2k√(7)=-2√(7)\\\\~~~~ k=(-2√(7))/(2√(7))\\\\ \boxed{\bf k =-1}`