root11-root7/root11+root7=a-b root77
Answers
Answer:
a=
2
9
,b=
2
1
Step-by-step explanation:
LHS=\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}LHS=
11
+
7
11
−
7
/* Rationalising the denominator, we get
=\frac{(\sqrt{11}-\sqrt{7})(\sqrt{11}-\sqrt{7})}{(\sqrt{11}+\sqrt{7})(\sqrt{11}-\sqrt{7})}=
(
11
+
7
)(
11
−
7
)
(
11
−
7
)(
11
−
7
)
=\frac{(\sqrt{11}-\sqrt{7})^{2}}{(\sqrt{11})^{2}-(\sqrt{7})^{2}}=
(
11
)
2
−(
7
)
2
(
11
−
7
)
2
=\frac{11+7-2\times \sqrt{11}\times \sqrt{7}}{11-7}=
11−7
11+7−2×
11
×
7
/* By algebraic identities:
i) (a-b)² = a²+b²-2ab
ii) (a+b)(a-b) = a² - b² */
= \frac{18-2\sqrt{77}}{4}=
4
18−2
77
=\frac{2(9-\sqrt{77})}{4}=
4
2(9−
77
)
=\frac{9-\sqrt{77}}{2}=
2
9−
77
\begin{gathered}=\frac{9}{2}-\frac{\sqrt{77}}{2}\\=RHS\end{gathered}
=
2
9
−
2
77
=RHS
Therefore,
\begin{gathered}\frac{9}{2}-\frac{\sqrt{77}}{2}\\=a-b\sqrt{77}\end{gathered}
2
9
−
2
77
=a−b
77
/* Compare both sides, we get
a=\frac{9}{2},\:b=\frac{1}{2}a=
2
9
,b=
2
1
Step-by-step explanation:
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Answer:
STEP
1
:
-10
Simplify ———
39
Equation at the end of step
1
:
6 -22 26 -10
(——•———)-(———•———)
55 9 125 39
STEP
2
:
26
Simplify ———
125
Equation at the end of step
2
:
6 -22 26 -10
(—— • ———) - (——— • ———)
55 9 125 39
STEP
3
:
-22
Simplify ———
9
Equation at the end of step
3
:
6 -22 -4
(—— • ———) - ——
55 9 75
STEP
4
:
6
Simplify ——
55
Equation at the end of step
4
:
6 -22 -4
(—— • ———) - ——
55 9 75
STEP
5
:
Calculating the Least Common Multiple
5.1 Find the Least Common Multiple
The left denominator is : 15
The right denominator is : 75
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
3 1 1 1
5 1 2 2
Product of all
Prime Factors 15 75 75
Least Common Multiple:
75
Calculating Multipliers :
5.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5
Right_M = L.C.M / R_Deno = 1