if √26-7√3 / √14+5√3 = a +b√3, then what is the value of (a - b)?
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Answer:
Correct option is
A
7
We have,
∣
∣
∣
∣
a
∣
∣
∣
∣
=
26
∣
∣
∣
∣
b
∣
∣
∣
∣
=7
∣
∣
∣
∣
a
×
b
∣
∣
∣
∣
=35
Since,
∣
∣
∣
∣
a
×
b
∣
∣
∣
∣
=
∣
∣
∣
∣
a
∣
∣
∣
∣
∣
∣
∣
∣
b
∣
∣
∣
∣
sinθ
Thus,
35=
26
×7×sinθ
sinθ=
26
5
We know that
a
⋅
b
=
∣
∣
∣
∣
a
∣
∣
∣
∣
∣
∣
∣
∣
b
∣
∣
∣
∣
cosθ
Therefore,
a
⋅
b
=
26
×7×
1−sin
2
θ
a
⋅
b
=
26
×7×
1−
26
25
a
⋅
b
=
26
×7×
26
1
a
⋅
b
=7
Hence, this is the answer.
Step-by-step explanation:
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