Question

Find the value of a and b if root 7 - root 3 / root 7 + root 3 = a - b root 21

Answer 1

Solution:

LHS = (√7-√3)/(√7+√3)

multiply numerator and denominator by (√7-√3),we get

= [(√7-√3)(√7-√3)]/[(√7+√3)(√7-√3)]

= (√7-√3)²/[(√7)²-(√3)²]

= [(√7)²+(√3)²-2(√7)(√3)]/(7-3)

= (7+3-2√21)/4

= (10-2√21)/4

= 10/4 -(2√21)/4

= 5/2 - √21/4

= a-b√21

Therefore,

a = 5/2 , b = 1/4

•••

Answer 2

The value of a is 5/2 and b is 1/2.

Step-by-step explanation:

The given equation is

$\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}=a-b\sqrt{21}$

Rationalize LHS,

$LHS=\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}\times \dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}-\sqrt{3}}$

$LHS=\dfrac{(\sqrt{7}-\sqrt{3})^2}{\sqrt{7}^2-\sqrt{3}^2}$

$LHS=\dfrac{\sqrt{7}^2-2\sqrt{7}\sqrt{3}+\sqrt{3}^2}{7-3}$

$LHS=\dfrac{7-2\sqrt{21}+3}{4}$

$LHS=\dfrac{10-2\sqrt{21}}{4}$

$LHS=\dfrac{10}{4}-\dfrac{2\sqrt{21}}{4}$

$LHS=\dfrac{5}{2}-\dfrac{1}{2}\sqrt{21}$

Compare LHS and RHS,

$\dfrac{5}{2}-\dfrac{1}{2}\sqrt{21}=a-b\sqrt{21}$

$a=\dfrac{5}{2},b=\dfrac{1}{2}$

Therefore, the value of a is 5/2 and b is 1/2.

#Learn more

√3+7/√3-7 + √2-3/√3+7. rationalize....​

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