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Integers — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSIntegers3 Marks
Question
If $\triangle$ is an operation such that for integers a and b we have a $\triangle b = a \times b -2 \times a \times b + b \times b (-a) \times b + b \times b$ then find. Also show that $4\triangle(-3)\neq(-3)\triangle4$ and$(-7)\triangle(-1)\neq(-1)\triangle(-7)$
✓

Answer

Now, put $a = (-7)$ and $b = (-1)\Rightarrow (-7)\triangle (-1)$
$= (-7) \times (-1) -2 \times (-7) \times (-1) + (-1) \times (-1){-(-7)} \times (-1) + (-1) \times (-1)$
$= 7 - 14 + 1 \times 7 \times (-1) + 1$
$= 7 - 4 - 7 + 1 - 13$ Now, put $a$
$= (-1)$ and $b = (-7)$
$= (-1) \triangle (-7)$
$= (-1) \times (-7) -2 \times (-1) \times (-7) + (-7) \times (-7) \{-(-1)\} \times (-7) + (-7) \times (-7)$
$= 7 - 14 + 49(1) \times (-7) + 49$
$= 7 - 14 - 343 + 49$
$= -301$ Clearly,
$=(-7)\triangle(-1)\neq(-1)\triangle(-7)$

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