If a, b are rationals, find the value of a and b if av2 +bV3 - V98 + V108 – V48 – V72
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Answer:
\begin{gathered}a \sqrt{2} + b \sqrt{3} = \sqrt{98} + \sqrt{108} - \sqrt{48} - \sqrt{72} \\ a \sqrt{2} + b \sqrt{3} = \sqrt{2 \times 7 \times 7} + \sqrt{2 \times 2 \times 3 \times 3 \times 3} - \sqrt{2 \times 2 \times 2 \times 2 \times 3} - \sqrt{2 \times 2 \times 2 \times 3 \times 3} \\ a \sqrt{2} + b \sqrt{3} = 7 \sqrt{2 } + 6 \sqrt{3} - 4 \sqrt{3} - 6 \sqrt{2} \\ a \sqrt{2} + b \sqrt{3} = \sqrt{2} + 2 \sqrt{3} \\ \end{gathered}
a
2
+b
3
=
98
+
108
−
48
−
72
a
2
+b
3
=
2×7×7
+
2×2×3×3×3
−
2×2×2×2×3
−
2×2×2×3×3
a
2
+b
3
=7
2
+6
3
−4
3
−6
2
a
2
+b
3
=
2
+2
3
Therefore, a= 1 and b= 2
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