Answer:
Statement 1 is true; Statement 2 is false.
Step-by-step explanation:
Statement 1:
√12 - √8 = a
Let's use the given value of √12 + √8 ,that is, 4/ a.
If we multiply both the expressions such that their Left Hand Sides get multiplies together and Right Hand Sides together:
=> (√12- √8)(√12 + √8) = a × 4/a
<em>On</em><em> </em><em>the</em><em> </em><em>LHS</em><em>,</em><em> </em>
<em>identity</em><em> </em><em>used</em><em>:</em>
<em>(</em><em>a-b</em><em>)</em><em>(</em><em>a</em><em>+</em><em>b</em><em>)</em><em> </em><em>=</em><em> </em><em>a</em><em>²</em><em>-</em><em>b</em><em>²</em>
<em>On</em><em> </em><em>the</em><em> </em><em>RHS</em><em>:</em>
<em>a</em><em> </em><em>gets</em><em> </em><em>canceled</em><em> </em><em>due</em><em> </em><em>to</em><em> </em><em>its</em><em> </em><em>presence</em><em> </em><em>in</em><em> </em><em>both</em><em> </em><em>the</em><em> </em><em>numerator</em><em> </em><em>as</em><em> </em><em>well</em><em> </em><em>as</em><em> </em><em>the</em><em> </em><em>denominator</em><em>.</em><em> </em>
=> 12 - 8 = 4
=> 4 = 4
That's it!
We got LHS = RHS, that approves the existence of the given statement.
___________________
Statement 2:
<em>"</em><em>a + √b is called the rationalizing factor of c + √d if their product is 1</em><em>"</em>
That's not entirely right!
The correct statement would be:
<em>"</em><em> </em><em>a + √b is called the rationalizing factor of c + √d if their product is </em><em><u>a</u></em><em><u> </u></em><u><em>rational</em><em> </em><em>number</em><em> </em><em>.</em></u><em><u>"</u></em>
Since, rationalizing has got nothing to do with 1, (1 is just another rational number), even if we get 2 by their multiplication, it will be called rationalizing as long as we're getting a rational number.
___________________
Answer:
Hence, I'd say:
Statement 1 is correct but Statement 2 isn't.
That's the third option.
